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13 June, 10:47

At a competition with 6 runners, 6 medals are awarded for first place through sixth place. Each medal is different. How many ways are there to award the medals? Decide if the situation involves permutation or a combination, and then find the number of ways to award the medals

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  1. 13 June, 10:59
    0
    There are 720 ways to award the medals

    Step-by-step explanation:

    * Lets explain the difference between permutations and combinations

    - Both permutations and combinations are collections of objects

    - Permutations are for lists (order matters)

    - Combinations are for groups (order doesn't matter)

    - A permutation is an ordered combination.

    - Permutation is nPr, where n is the total number and r is the number

    of choices

    # Example: chose the first three students from the group of 10

    students, n = 10 and r = 3, then 10P3 is 720

    - Combinations is nCr, where n is the total number and r is the number

    of the choices

    # Example: chose a group of three students from the group of 10

    students n = 10 and r = 3, then 10C3 is 120

    * Lets solve the problem

    - There are six runner

    - There are 6 medals awarded for first place through sixth place

    - Each medal is different

    - The order is important because they arranged from 1st position to

    the 6th position

    ∴ We will use the permutation

    ∵ There are 6 medals for 6 runners

    ∵ 6P6 = 6 * 5 * 4 * 3 * 2 * 1 = 720

    ∴ There are 720 ways to award the medals
  2. 13 June, 11:17
    0
    permutation; 720 ~apex
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