Question

In a 12-person team with a batting order for 7 players, what is the number of possibilities?

a) 792

b) 924

c) 1,155

d) 1,320

Answer 1

The number of possibilities for the batting order of a 12-person team with 7 players in the batting order is 665,280.

Step-by-step explanation:

To find the number of possibilities for the batting order of a 12-person team with 7 players in the batting order, we can use the concept of permutations. A permutation represents the number of ways to arrange a set of objects in a certain order. In this case, we want to find the number of permutations of 7 players selected from a pool of 12 players. The formula for permutations is nPr = n! / (n - r)!, where n is the total number of objects and r is the number of objects to be selected. Plugging in the values, we have 12P7 = 12! / (12 - 7)! = 12! / 5! = (12 * 11 * 10 * 9 * 8 * 7 * 6) / (5 * 4 * 3 * 2 * 1) = 12 * 11 * 10 * 9 * 8 * 7 = 665,280 possibilities.