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  1. #1

    افتراضي تمارين مع الحلول في التباديل والتوافيق

    السلام عليكم
    إليكم هذه التمارين المتنوعة في التباديل والتوافيق

    IV. COMBINATION


    1. In how many ways can 3 books be selected from 8 different books? [56]
    2. In how many ways can a set of 2 boys and 3 girls be selected from 5 boys and 4 girls? [40]
    3. How many different selections can be made by taking 3 of the digits 4, 5, 6, 7, 8, 9 ? [20]
    4. In how many ways can a committee of 4 men and 5 boys be formed from 8 men and 7 boys ? [1470]
    5. From 8 soldiers, 7 sailors and 5 airmen how many sets can be formed each containing 5 soldiers, 4 sailors and 3 airmen ? [19600]
    6. In how many ways can 8 boys be divided into two sets containing 5 and 3 respectively? [56]
    7. A committe of 6 is to be selected from 10 people of whom A and B are two. How many committees can be formed (i) containing A and B, (ii) excluding A if B is included ? [70;140]
    8. In how many ways can 3 cards be selected from a pack of 52 playing cards if [i] at least one of them is an ace, [ii] not more then one is an ace ? [4804; 21808]
    9. In how many ways can a commitees of three men and 4 women be chosen from 6 men and 7 women? What proportion of these commitees contains a particular man and a particular women? [700; 1/7]
    10. A commitees of 7 politicians is chosen from 10 liberal members, 8 labor members and 5 independents. In how many ways can this be done so as to include exactly 1 independent and at least 3 liberal members and at least 1 labor member? [73080]
    11. An eleven is to be chosen from 15 cricketers of whom 5 are bowlers only.2 others are wicket keepers only and the rest are batsmen only.How many possibles elevens can be chosen which contain ( i ) 4 bowlers, 1 wicketkeeper and 6 batsmen, ( ii )at least 4 bowlers and at least 1 wicktkeeper? [280; 742]
    12. From 7 teachers and 5 pupils a commitee of 7 is to be formed. How many commitees can be selected if both teachers and pupils are represented and the teachers are in a majority? [595]
    13. From 4 oranges, 3bananas and 2 apples, how many selections of 5 pieces of fruit can be made, talking at least one of each kind? [98]
    14. In lotto, a frame contain the numbers 1 to 40 and we can select any 6 of these numbers. How many such combinations are possible? [3,838,380]
    15. In TAB betting, the "trifecta" pays on first three horses in correct order, the "quinella" pays on the first two horses in either orther. In a 10 horses race what is the possible number of (a) trifecta combination (b) quinella combinations? [720;45]
    16. In how many ways can a jury of 12 be chosen from 10 men and 7 women so that there are at least 6 men and not more than 4 women on each jury? [1946]
    17. In how many ways can a set of 3 or more be selected from 9 people? [466]
    18. In how many ways can n things be shared between 2 people. [2n - 2]
    19. In how many ways can a commitee of 3 men and 4 boys be chosen from 7 men and 6 boys so as not to include the youngest boy if the eldest man is serving? [375]
    20. How many ( i ) selections, ( ii ) arrangements consisting of 3 consonants and 2 vowels can be made from 8 consonants and 4 vowels? [336; 40320]
    21. In how many ways can 4 Physics books and 3 Mathematics books be arranged on a ****f if a selection is made from 6 different Physics books and 5 different Mathematics books? In how many of these arrangements are the Physics books together? [756,000; 86400]
    22. In how many ways can 3 boys and 2 girls be arranged in a row if a selection is made from 5 boys and 4 girls? In how many of these arrangements does a boy ocupy the middle position? [7200; 4320]
    23. How many words (arrangement of letters ), containing 3 consonants and 2 vowels, can be formed from the letters of the word promise ? [1440]
    26. The ratio of the number of combinations of (2n+2) different objects taken n at a time to the number of combinations of (2n-2) different objects taken n at a time is 99:7. Find the value of n. [5]
    27. In how many ways can 9 books be distributed amongst a man, a woman and the child, if the man receives 4, the woman 3 and the child 2? [1260]
    28. In how many ways can 8 boys be divided into two unequal sets? [92]
    29. In how many ways can 8 girls be divided into 4 sets of 2? [105]

    II. PERMUTATION I (LINEAR ARRANGEMENTS)


    1. How many different arrangements can be made by taking 3 letters of the word SUNDAY ?
    2. In how many ways can 5 boys be arranged in a row ?
    3. In how many ways can a first, second and third prize be awarded in a class of 8 students ?
    4. How many 5-digit numbers can be formed from the digits 2,3,5,6,8,9 if no digit can be used more than once in a number ? How many even numbers can be formed ?

    5. Find the value of (i) (ii) (iii)
    6. Find the value of (i) 6! (ii) 8! / 5!
    7. In how many ways can 4 consonants and 3 vowels be arranged in a row (a) so that the 3 vowels are always together, (b) so that the first and the last places are occupied by consonants.
    7a. There are 4 different mathematics books, 6 different physics books, and 2 different chemistry books are to be arranged on a ****f. How many different arrangements are possible if (a) the books in each category must all stand together , (b) only the mathematics books must stand together.
    8. In how many ways can four girls and three boys be arranged in a row so that (a) the boys are always together, (b) the girls and boys occupy alternate places ?
    9. In how many ways can 6 people be seated in a motor car if only 2 can occupy the driver's position ?
    10. In how many ways can 6 people be arranged in a circle if 2 particular people are always (a) together (b) separated.
    11. Father, mother and 6 children stand in a ring. In how many ways can they be arranged if father and mother are not to stand together.
    12. In how many ways can 5 boys and 3 women be arranged (a) in a row , (b) in a circle if both cases the women are always to stand together ?
    13. Four men and four women are to be seated alternately (a) in a row (b) at a round table. In how many ways can this be done ?
    14. How many even number of 4 digits can be forned with the figures 3,4,7,8 if (a) no figure is repeated , (b) repetitions are allowed.
    15. How many numbers greater than 4000 can be formed from the figures 3,5,7,8,9 ? (repetitions not allowed).
    16. In how many ways can the letters of the word PERMUTE be arranged if (i) the first and last places are occupied by consonants, (ii) the vowels and consonants occupy alternate places.
    17. If , find r.
    18. The number of arrangements of 2n+2 different objects taken n at a time is to the number of arrangements of 2n different objects taken n at a time as 14:15. Find the value of n.
    19. How many numbers of 7 digits can be formed from the digits 1,2,3,4,5,6,7 if (i) the numbers begins with 1 and ends with 2, (ii) there are not more than 2 digits between 1 and 2 ?
    20. If , find the value of n. [4]

    21. In how many ways can 5 different mathematics books, 4 different physics books and 2 different chemistry books be arranged on a ****f if the books in each subject are to be together.
    22. In how many can 3 men, 3 women and 3 boys be arranged in a row if the three boys are to remain together ?
    23. Find the number of arrangements of the letter in the word PENCILS if (i) E is next to I, (ii) E precedes I, (iii) there are three letters between E and I.
    24. In how many ways can the letters of the word PRINCIPLE be arranged? In what proportion of these arrangements do the letters P come together ? .
    25. In how many ways can the letters in PRECISION be arranged? In how many of these arrangements do the vowels occupy even places ?
    26. How many arrangements can be made by the letters of word DEFINITION (i) if the letters I do not occupy the first or last place, (ii) if the letters I are together?
    27. How many different arrangements of the letters in TOMATO are there, if the letters O are to be separated?
    28. A car can hold 3 people in the front seat and 4 in the back seat. In how many ways can 7 people be seated in the car if 2 particular people must sit in the back seat and 1 particular person is the driver?
    29. In how many ways can 4 people be accommodated if there are 4 rooms available?
    30. In how many ways can 8 oarsmen be seated in a eight-oared boat if 3 can row only on the stroke side and 3 can row only on the bow side ?
    31. Prove that (i) from the definition of .
    (ii) the formula for that .
    32. Prove that .
    33. In how many ways can 5 men and 5 women by arranged in a circle so that the men are separated? In how many ways can this be done if two particular women must not be next to a particular men.
    34. How many arrangements of the letters of the word PARRAMATTA are possible?

    ANSWERS:
    1. 120 2. 120 3. 336 4. 720; 360 5.(i) 120 (ii) 11800 (iii) 6720 6.(i) 720 (ii) 336
    7.(a) 720 (b) 1440 7a (a) 207360 (b) 8709120 8.(a) 720 (b) 144 9. 240 10.(a) 120
    (b) 48 (c) 72 11. 3600 12. (a) 4320 (b) 720 13.(a) 1152 (b) 144 14. (a) 12 (b) 128
    15. 216 16 (i)1720 (ii) 72 17. r=3 18. 3 19.(i) 120 (ii) 15 20. 4 21. 34560 22. 30240
    23. (i) 1440 (ii) 2520 (iii) 120 24. 90720, 22.2% 25. 181440; 1440 26. (i) 141120 (ii) 20160 27. 120 28. 288 29. 256 30. 1152 33. 2880; 864 34. 37800

    ومن يريد تمارين في الإحتمال وحساب المثلثات والتفاضل والتكامل هناك المزيد في هذه الوصلة
    http://www.saigon.com:8081/~tuan/math/

  2. #2
    تربوي مبدع
    تاريخ التسجيل
    Jan 2004
    الدولة
    كوكب الزهره
    المشاركات
    287

    افتراضي مشاركة: تمارين مع الحلول في التباديل والتوافيق

    شو هالخرااابيط؟

  3. #3

    افتراضي مشاركة: تمارين مع الحلول في التباديل والتوافيق

    جزاك الله خيرا أختي الفاضلة ..

    و لكن كما تعلمين أن الرياضيات معنا في السلطنة باللغة العربية هذا من جهة و من جهة أخرى فمستوى معظم الطلاب في الانجليزية لا يوصلهم لإلى درجة إعطائهم أسئلة بالانجليزية..

    شاكرا لك على هذه الأسئلة.

  4. #4

    افتراضي مشاركة: تمارين مع الحلول في التباديل والتوافيق

    شكرا لك
    أليس ممكنا أن يستفيد منها المعلمين ولو القليل منهم على الأقل وهم بدورهم يترجمونها للطلاب
    في الحقيقة كنت أود أن أترجمها ولكن ظروف الوقت
    ولكنني أعد أني سأعمل على ترجمتها قريبا إن شاء الله
    ولكم مني أزكى التحية

  5. #5

    افتراضي رد : تمارين مع الحلول في التباديل والتوافيق

    مشكوووووووووووور
    مشكوووووووووووووووووووور
    مشكوووووووووووووووووووور

  6. #6
    تربوي برونزي
    تاريخ التسجيل
    Jun 2005
    الدولة
    عاصمة الثقافة العربية
    المشاركات
    727

    افتراضي رد : تمارين مع الحلول في التباديل والتوافيق

    مشكووووووووووووووورة عزيزتي على التمارين
    ونحن في إنتظار كل ما هو مفيد وجديد

  7. #7
    تربوي برونزي
    تاريخ التسجيل
    Sep 2005
    الدولة
    Roses Land
    المشاركات
    662

    افتراضي رد : تمارين مع الحلول في التباديل والتوافيق

    على فكرة عجبتني الأسئلة خاصة أنها بلEnglish
    نتمنى إنك تدزيلنا المزيد منهم...........زز
    تحياتي........................ز

  8. #8
    تربوي موهوب
    تاريخ التسجيل
    Dec 2008
    المشاركات
    16

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    اسئلة جميلة خلنا نرفعها فوق

  9. #9

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    حن بالعربي ما فلحنــا لين نفلح بالإنجليزي !!
    ع العمووم ~ يسلموو .. ما تقصري عسى حد يستفيد منهن ~

  10. #10
    تربوي برونزي
    تاريخ التسجيل
    Mar 2011
    الدولة
    بينْ غيمهہِ حزنْ وَ قطرهہِ فرح ..
    المشاركات
    708

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    مشكوره بس يااختي احنا باللغه العربيه ندرس الرياضيات

    شاكره لك تعاووونك ونتمنى لك المزيد والمزيد من العطاء

  11. #11

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    نريد الترجمه لو سمحتتتو

  12. #12

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    ناااااااااايس
    الصراااحة تحفة الاسئلة معلمتنا مال الرياضيات غير الامثلة و التدريبات اللي ف الكتاب ماشي غيرهم
    ما تجيب لنا تدريبات خارجية

  13. #13

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    thanks
    gad bless you

  14. #14
    تربوي موهوب
    تاريخ التسجيل
    Jan 2012
    المشاركات
    13

    افتراضي رد: تمارين مع الحلول في التباديل والتوافيق

    Thank U very Much for those questions
    It is almost clear 90%

ط§ظ„ط¹ظ„ط§ظ…ط§طھ ط§ظ„ظ…ط±ط¬ط¹ظٹط©

ط§ظ„ط¹ظ„ط§ظ…ط§طھ ط§ظ„ظ…ط±ط¬ط¹ظٹط©

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