Probability - Baseball Team

[ntamhane]

A baseball team consists of 20 players. 5 of whom are pitchers and 15 of whom are position players. If the order consists of 8 different position players and 1 pitcher, and if the pitcher always bats last in the order, which of the following expressions gives the number of possible different batting orders for this baseball team?

A. (15!)*(5)/8!
B. (15!)*(5)/7!
C. (15!)*(5!)/7!
D. 15!*5
E.20!

I go the answer [spoiler](15!)*5/8!*7! which is not a choice.[/spoiler] where am i going wrong

[Frankenstein]

Hi,
I guess you are just picking 8 players from 15. So, you used 15C8. But, here we have to arrange those 8 players. This can be done in 15P8, and the last position can be filled in 5 ways.
So, the number of ways should be (15P8)*5 = 15!*5/7!

Hence, B

[krishnasty]

I guess you are taking combination...
we have to 'arrange' players here...hence, use permutation