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Math Help - Combinations

  1. #1
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    Combinations

    A pharmacist uses 5 separate weights: 1 g, 2g, 4 g, 8 g and 16 g. If the pharmacist can combine these weights to create new weights, how many different weights are possible?
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  2. #2
    Super Member Aryth's Avatar
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    Well, it's a simple problem. You could just find the possible combinations of picking differing sets of weight. Combinations of 1 weight picked from 5, combinations of 2 weights picked from 5, combinations of 3 weights picked from 5... Etc. You use the following formula for n being the total number of weights and r being the number of weights you're choosing:

    C^n_r = \frac{n!}{r!(n - r)!}

    For r=0:

    C^5_0 = \frac{5!}{0!(5)!}

    = 1

    For r=1:

    C^5_1 = \frac{5!}{1!(4)!}

    = 5

    For r=2:

    C^5_2 = \frac{5!}{2!(3)!}

    = 10

    For r=3:

    C^5_3 = \frac{5!}{3!(2)!}

     = 10

    For r=4:

    C^5_4 = \frac{5!}{4!(1)!}

    = 5

    For r=5:

    C^5_5 = \frac{5!}{5!(0)!}

    = 1

    Now you add them all together:

    Total = 1 + 5 + 10 + 10 + 5 + 1 = 32

    That tells you that there are 32 possible combinations
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