On an American League baseball team with 15 field players and 10 pitchers, the manager must select for the starting line-up, 8 field players, 1 pitcher and 1 designated hitter. A starting line-up specifies the players for these positions and the positions in a batting order for the 8 field players and designated hitter. If the designated hitter must be chosen among all the possible field players, how many possible starting line-ups are there.

There are 18,162,144,000 possible starting line-ups

Step-by-step explanation:

The order in which the player are chosen is important, as if two player exchange places, we have a new batting order. So we use the permutations formula to solve this question.

Permutations formula:

The number of possible permutations of x elements from a set of n elements is given by the following formula:

In this question:

Batting order:

9 batters(8 field + the designated hitter) from a set of 15. So

Pitcher:

1 from a set of 10. So

Total:

There are 18,162,144,000 possible starting line-ups

-7/8

step-by-step explanation:

instead of subtracting you add the -6/8 and -1/8