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30 December, 05:22

How many ways can 6 different prize be distributed equally among three superior students?

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  1. 30 December, 06:04
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    There are 90 ways to distribute the prizes

    Step-by-step explanation:

    * Lets explain how to solve the problem

    - There are 6 different prize distributed equally among 3 super students

    ∵ There are 6 prize are to be equally distributed among 3 students

    ∴ Each student will get ⇒ 6 : 3 = 2

    ∴ Each student takes 2 prize

    * Order doesn't matter here because the 3 students are super

    so we can start with any one of them

    # The 1st student will get 2 prize from 6

    ∴ The choices = 6C2

    # The 2nd student will get 2 prize from remaining 4 prize

    ∴ The choices = 4C2

    # The 3rd student will get 2 prize from remaining 2 prize

    ∴ The choices = 2C2

    * To find the total choices multiply the three choices above

    ∴ The total choices = 6C2 * 4C2 * 2C2

    ∴ The total choices = 15 * 6 * 1 = 90 choices

    * There are 90 ways to distribute the prizes
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