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  • Question
  • In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?


  • Options
  • A. 266
  • B. 5040
  • C. 11760
  • D. 86400
  • E. None of these

  • Correct Answer
  • 11760 

    Explanation
    Required number of ways = (8C5 x 10C6)
    = (8C3 x 10C4)
    = ❨ 8 x 7 x 6 x 10 x 9 x 8 x 7
    3 x 2 x 1 4 x 3 x 2 x 1
    = 11760.

  • Permutation and Combination problems


    Search Results


    • 1. In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?

    • Options
    • A. 360
    • B. 480
    • C. 720
    • D. 5040
    • E. None of these
    • Discuss
    • 2. In how many different ways can the letters of the word 'DETAIL' be arranged in such a way that the vowels occupy only the odd positions?

    • Options
    • A. 32
    • B. 48
    • C. 36
    • D. 60
    • E. 120
    • Discuss
    • 3. In how many ways can the letters of the word 'LEADER' be arranged?

    • Options
    • A. 72
    • B. 144
    • C. 360
    • D. 720
    • E. None of these
    • Discuss
    • 4. Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

    • Options
    • A. 210
    • B. 1050
    • C. 25200
    • D. 21400
    • E. None of these
    • Discuss
    • 5. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?

    • Options
    • A. 32
    • B. 48
    • C. 64
    • D. 96
    • E. None of these
    • Discuss
    • 6. In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

    • Options
    • A. 810
    • B. 1440
    • C. 2880
    • D. 50400
    • E. 5760
    • Discuss
    • 7. How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?

    • Options
    • A. 5
    • B. 10
    • C. 15
    • D. 20
    • Discuss
    • 8. In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?

    • Options
    • A. 63
    • B. 90
    • C. 126
    • D. 45
    • E. 135
    • Discuss
    • 9. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?

    • Options
    • A. 159
    • B. 194
    • C. 205
    • D. 209
    • E. None of these
    • Discuss
    • 10. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?

    • Options
    • A. 10080
    • B. 4989600
    • C. 120960
    • D. None of these
    • Discuss


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