Question

A baseball team has 15 members, 3 of whom always play and bat at the top of the batting order. For the game Sunday, the starting lineup of nine players will be filled out from the remaining members and a batting order will be set.

Answer 1

A line-up has 9 members, of which the first three have been determined. Therefore it is out of 12 remaining we choose 6. The number of ways is C(12,6), or 12 choose 6.

The formula for "n choose r", or C(n,r) is
C(n,r)=n!/(r!(n-r)!)

So "12 choose 6"
= 12!/(6!(12-6)!)
= 12*11*10*9*8*7/(1*2*3*4*5*6)
= 924.