Question

Eleven people are entered in a race. If there are no ties, in how many ways can the first two places come out?

Answer 1

5.5

Answer 2

110

11nPr2

Answer 3

[AI-generated answer — Explain Bot]

To determine the number of ways the first two places can come out, we need to calculate the permutations of the 11 people taken 2 at a time.

Permutations refer to the arrangement of objects or people in a specific order. The formula to calculate permutations is:

P(n, r) = n! / (n-r)!

Where n represents the total number of objects (or people) and r represents the number of objects (or people) to be selected.

In this case, we have 11 people (n) and we want to select 2 people (r).

P(11, 2) = 11! / (11-2)!
= 11! / 9!
= (11 * 10 * 9!) / 9!
= 11 * 10
= 110

Therefore, there are 110 different ways the first two places can come out in the race.