Question

Kai is coaching a little league team. When he chooses 9 players for his batting lineup out of his 17 players, is this an example of a combination or a permutation?

a) Combination
b) Permutation

Answer 1

This is an example of a combination, where the order does not matter.

Step-by-step explanation:

This is an example of a combination.

A combination is a selection of items where the order does not matter. In this case, Kai is choosing 9 players for his lineup out of 17 players. The order in which they are selected does not matter, as long as he chooses 9 players.

If this were a permutation, the order of the players in the lineup would matter. For example, if Kai was choosing the players for specific positions in the lineup, it would be a permutation. Here, the absence of positional allocation highlights the essence of a combination, emphasizing the mere selection of players for the lineup, exemplifying the concept where order remains inconsequential within the context of Kai's player selection process.