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  • Question
  • 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

  • Correct Answer
  • 20 

    Explanation
    Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.

    The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.

    The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.

    ∴ Required number of numbers = (1 x 5 x 4) = 20.


    Permutation and Combination problems


    Search Results


    • 1. 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
    • 2. 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
    • Discuss
    • 3. 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
    • 4. 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
    • 5. 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
    • 6. 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
    • 7. 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
    • 8. 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
    • 9. How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?

    • Options
    • A. 40
    • B. 400
    • C. 5040
    • D. 2520
    • Discuss
    • 10. From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

    • Options
    • A. 564
    • B. 645
    • C. 735
    • D. 756
    • E. None of these
    • Discuss


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