Question

Nineteen students play on a baseball team .how many ways can the batting order of 10 players be arranged?

Answer 1

Start at 19 and work your way down until you have counted 10 players.
19 * 18 * 17 * 16 * 15 * 14 * 13 * 12 * 11 * 10

The rest cancels out.

Answer 2

Answer: The required number of ways is 335221286400.

Step-by-step explanation: Given that nineteen students play on a baseball team.

We are to calculate the number of ways in which the batting order of 10 players be arranged.

Since it is a situation of arrangement, the total number of ways will be equal to the permutation of 19 taken 10 at a time.

The formula for the number of permutations of n things taken r ata time is given by

`^nP_r=(n!)/((n-r)!).`

From the given information, we have

n = 19 and r = 10.

Therefore, the number of arrangements is given by

`^(19)C_(10)\\\\\\=(19!)/((19-10)!)\\\\\\=(19*18*17*16*15*14*13*12*11*10*9!)/(9!)\\\\\\=19*18*17*16*15*14*13*12*11*10\\\\=335221286400.`

Thus, the required number of ways is 335221286400.