Statistics. Suppose you are the coach of a church basketball team and are asked how many ways?

you can assign positions to your players (that would be 5 different positions) with a roster of 11 players. Assume that any player can go into any position. How many possible ways can you position your players?

Statistics. Suppose you are the coach of a church basketball team and are asked how many ways?
If you have n objects there are n! permutations of these objects.


If you have n objects and select r of them you have n! / (n - r)! permutations of the r objects. This can be written as n P r.





here we have 11 P 5


= 11! / (11 - 5)! = 11 * 10 * 9 * 8 * 7


= 55440
Reply:Assuming the question is how many different 5-person lineups one can derive from an 11-player roster, then the answer depends on whether you want to differentiate lineups consisting of the same 5 players but arranged in a different order.





If so, then the answer can be found by calculating 11P5, which is 11!/(11-5)!, or 11*10*9*8*7 which is 55,440.





If arrangement is irrelevant, then you would calculate 11C5, which means you divide the above answer by 5! (5*4*3*2*1=120), which reduces your number of distinct lineups to 462.
Reply:P(11, 5) = 55,440


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Ideas: You have 5 different positions to fill players. So, you can have 11 choices to fill the first position, 10 the second position, and so on. 11*10*9*8*7 = 55,440
Reply:11 x 10 x 9 x 8 x 7 different ways to do it, or 55440 possibilities, also expressed as 11!/6!
Reply:396. Easy Peasy.

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