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Math Help - How many ways can i arrange these numbers?

  1. #1
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    How many ways can i arrange these numbers?

    1,2,3,4,5,5


    how many 4 digit numbers can i arrange the above 6 digits into?

    I break it up into 3 cases:

    case 1: 0 occurence of 5 : 1,2,3,4 = 4! ways = 24 ways

    Case 2: 1 occurence of 5: 5xxx = 4C3 * 4! = 96 ways

    Case 3 : 2 occurence of 5: 55xx = 4C2 * 4!/2! = 72 ways

    Total = 192 ways.

    Am I correct?
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  2. #2
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    Quote Originally Posted by chopet View Post
    1,2,3,4,5,5--how many 4 digit numbers can i arrange the above 6 digits into? Total = 192 ways. Am I correct?
    Yes that is correct.
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