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    Question

    How many different nine digit numbers can be formed

    from the number 66 55 99 222 by rearranging its digits so that the odd digits occupy even positions only?
    A 70 Correct Answer Incorrect Answer
    B 1040 Correct Answer Incorrect Answer
    C 120 Correct Answer Incorrect Answer
    D 720 Correct Answer Incorrect Answer
    E 60 Correct Answer Incorrect Answer

    Solution

    Number of even places = 4 Number of even digits = 5 (6,6,2,2,2) Number of odd places = 5 Number of odd digits = 4 (5,5,9,9) Since 5 & 9 are repeated two times odd  digits can be arranged in 4!/(2!×2! )  = 6 ways Since 6 is repeated two times & 2 is repeated three times  even digits can be arranged in  5!/(2! ×3!)  = 10 ways Hence, the required number of ways = 6 × 10 = 60 ways.

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