A baseball team has 13 players; how many possible batting orders can the coach make if there are 9 players in the batting lineup?Hello can you help with this problem i try different ways to solve it but it is not match with my answers

A. 235,368
B. 1,235,520
C. 879,523
D. 514,874
Thank you so much

13P9 but that is not one of the choices. Typo?

However, 1,235,520 = 13P6

A baseball team has 13 players; how many possible batting orders can the coach make if there are 9 players in the batting lineup?


A. 235,368
B. 1,235,520
C. 879,523
D. 514,874

A is the answer

To find the number of possible batting orders, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.

In this case, we have 13 players and we need to select 9 of them for the batting lineup. So, we need to find the number of permutations of 13 players taken 9 at a time.

The formula for permutations is given by: P(n, r) = n! / (n-r)!

n = 13 (total number of players)
r = 9 (number of players in the batting lineup)

Substituting the values into the formula, we have:

P(13, 9) = 13! / (13-9)!
= 13! / 4!

Now, let's calculate the factorial values:
13! = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1

4! = 4 * 3 * 2 * 1

Now, we can simplify the expression:

13! / 4! = (13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / (4 * 3 * 2 * 1)

Cancel out the common terms:

= 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5

Calculating the expression, we get:

= 235,368

So, the correct answer is A. 235,368.