MATH

A hockey game is preparing for a group photo. The team has 1 goalie, 4 defense, and 7 forwards. The photographer wants two rows of six players. How many ways can the team arrange six players in the front row with at most 2 defense?

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  1. case1: no defence in 1st row
    - we can choose any 6 of the 8 players
    = C(8,6) = 28

    case2: 1 defence
    - four ways to choose the defenseman, choose 5 from the remaining 8
    = 4 x C( 8,5) = = 224
    Case3 : 2 defense
    = C(4,2) x C(8,4) = 420

    total = 28+224+420 = 672 for choosing the 6

    but you wanted the number of ways to arrange them ...
    number of ways = 672 x 6! = 483,840

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