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?

Answer 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

Answer 2

You are literally a life saver, thank you so so so so so so much!!