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  • Question
  • Out of seven consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed ?


  • Options
  • A. 25200
  • B. 25000
  • C. 25225
  • D. 24752

  • Correct Answer
  • 25200 

    Explanation

    Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4) =(  C 3 7 × C 2 4  ) = 210.

    Number of groups, each having 3 consonants and 2 vowels =210

    Each group contains 5 letters.

    Number of ways of arranging 5 letters among themselves = 5! = 120. 

    Required number of words = (210 x 120) = 25200.

  • Tags: CAT, Bank Exams, Bank PO, Bank Clerk

    Permutation and Combination problems


    Search Results


    • 1. 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. 15
    • B. 20
    • C. 5
    • D. 10
    • Discuss
    • 2. A box contains 5 green, 4 yellow and 5 white pearls. Four pearls are drawn at random. What is the probability that they are not of the same colour ? A) 11/91 B) 4/11 C) 1/11 D) 90/91

    • Options
    • A. Option A
    • B. Option B
    • C. Option C
    • D. Option D
    • Discuss
    • 3. How many more words can be formed by using the letters of the given word 'CREATIVITY'?

    • Options
    • A. 851250
    • B. 751210
    • C. 362880
    • D. 907200
    • Discuss
    • 4. The ratio of the members of blue to red balls in abag is constant. When there were 44 red balls, the number of blue balls was 36. If the number of blue balls is 54, how many red balls will be in the bag?

    • Options
    • A. 68
    • B. 32
    • C. 64
    • D. 66
    • Discuss
    • 5. If each vowel of the word NICELY is changed to the next letter in the English alphabetical series and each consonant is changed to the previous letter in the English alphabetical series and then the alphabets are arranged in alphabetical order, which of the following will be fourth from the left?

    • Options
    • A. M
    • B. J
    • C. B
    • D. O
    • Discuss
    • 6. A class has 8 football players. A 5-member team and a captain will be selected out of these 8 players. How many different selections can be made ?

    • Options
    • A. 210
    • B. 168
    • C. 1260
    • D. 10!/6!
    • Discuss
    • 7. 36 identical books must be arranged in rows with the same number of books in each row. Each row must contain at least three books and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible ?

    • Options
    • A. 5
    • B. 6
    • C. 7
    • D. 8
    • Discuss
    • 8. How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?

    • Options
    • A. 120
    • B. 240
    • C. 256
    • D. 360
    • 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. 209
    • B. 290
    • C. 200
    • D. 208
    • Discuss
    • 10. How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never beings separated?

    • Options
    • A. 1440
    • B. 720
    • C. 360
    • D. 640
    • Discuss


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