SOLUTION: Please help me understand how to answer this question. Thanks! "As a basketball coach, how many possible ways can you position your players if you have a roster of ten and five

Question 316102: Please help me understand how to answer this question. Thanks!
"As a basketball coach, how many possible ways can you position your players if you have a roster of ten and five different positions?"

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You have ten selections and five slots to place them. Let's assume that order matters. So for the first position, you have ten choices. For the second, you have 9 choices (since that first player can't play two positions). The third will have 8 choices, the 4th will have 7 choices, and the fifth position will have 6 choices.

Now just multiply all these choices out to get: 10*9*8*7*6 = 30240

So there are 30240 different lineups.

Another formal way is to use the permutation formula, but we basically follow the same logic. If we were to use the permutation formula

, we'll plug in n=10 and r=5. After a bit of work, you'll end up with 10*9*8*7*6 = 30240 which is the same answer.
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