JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Definition of permutation, Number of permutations with or without repetition, Conditional permutations

  • question_answer
    How many numbers greater than hundred and divisible by 5 can be made from the digits 3, 4, 5, 6, if no digit is repeated [AMU 1999]

    A) 6

    B) 12

    C) 24

    D) 30

    Correct Answer: B

    Solution :

    Numbers which are divisible by 5 have ?5? fixed in extreme right place
    3 Digit Numbers 4 Digit Numbers
    H T U Th H T U
    × × 5 × × × 5
    \[^{3}{{P}_{2}}\] ways \[^{3}{{P}_{3}}\] ways
    = \[\frac{3!}{1!}\]   = \[\,3\times 2\] = \[\frac{3!}{0!}\]  =  \[3\times 2\]
    \[\Rightarrow \] Total ways = 12.


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