Question

The manager of a Little League baseball team has picked the nine starting players for a game. How many different batting orders are possible under each of the following conditions?
(a)there are no restrictions.
(b) the pitcher must bat last
(c) the pitchrmust bat last, the atcher eghth, and the shortstop first.

Answer 1

(a) No restrictions, so it is 9! = 362880

(b) Pitcher is last, so you fix pitcher at the 9th position. So the first 8 positions, you have 8 ways of arranging them. So, you'll get 8! * 1 = 40320

(c) S _ _ _ _ _ _ A P
here, you have fixed 3 positions already so all is 1, 1, 1
then you'll have 6 players left to arrange.
so, you'll get 6! * 1 * 1 * 1 = 720

Answer 2

thank you.