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March 26, 2017

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Diane has one stamp of each positive integer value 1 cent through 9 cents, inclusive. She wants to put 10 cents worth of postage in a row across the top of an envelope. If arrangements of the same stamps in different order are considered different, how many arrangements are possible?

  • Math - ,

    Make a list of combinations.

    2 stamps: 1,9
    number of ways to arrange = 2
    3 stamps: 1,2,7 - 1,3,6 - 1,4,5 - 2,3,5
    number of ways to arrange = 4(3!) = 24
    4 stamps: 1,2,3,4 - that is all of them
    number of ways to arrange = 1(4!) = 24

    total number of ways = 2+24+24 = 50

  • Math - ,

    Try doing it with casework.
    Case: 1
    1,9 x2
    2,8 x2
    3,7 x2
    4,6 x2
    2+2+2+2=8.
    That's it for case one since Diane only has one stamp for each.
    Case: 2
    1,2,7 x6
    1,3,6 x6
    1,4,5 x6
    2,3,5 x6
    6+6+6+6=24.
    Case: 3
    1,2,3,4 x24
    The total answer is 8+24+24=56.

  • Math - ,

    The answer is 56

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