A softball coach needs to choose 9 players to be in the batting lineup for the next game. There are 4 freshmen, 5 sophomores, 6 juniors, and 5 seniors on the team. Step 1 of 2 : How many ways can the batting order be chosen if the coach wants no more than 2 freshmen to be in the lineup

The batting order can be chosen in 6,572,966,400 ways.

Step-by-step explanation:

The order in which the players are in the lineup is important. That is, if we exchange two players positions in the batting order, we have an entire new batting order. So the permutations formula is used 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:

No more than 2 freshmen

Either no freshmen, 1 freshmen or two freshman.

No freshmen:

9 players from a set of 16(sophmores, juniors and seniors).

1 freshmen:

One freshmen, from a set of 4.

8 non-freshmen, from a set of 16. So

2 freshmen:

2 freshmen, from a set of 4.

7 non-freshmen, from a set of 16.

Total:

The batting order can be chosen in 6,572,966,400 ways.

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