Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?

a.) The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

b.) The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.

c.) The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

d.) The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.

Question

Julius

Mathematics

30 August, 01:26

Mark, Chase, and Beatrice are running a 100-meter race. Which list represents the sample space of all the possible ways in which the three runners can win first, second, and third places? If there were four runners and three positions to be won, what would the sample size be?

a.) The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

b.) The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 24.

c.) The sample space is {MBC, BCM, CMB}. If there were four runners, the sample size would be 4.

d.) The sample space is {MBC, MCB, BCM, BMC, CBM, CMB}. If there were four runners, the sample size would be 16.

+3

Answers (1)

Know the Answer?

Wilson Carpenter · Answer 1

Permutation problem.

number of permutations = n!

Here, there are three runners, so sample space size = 3!=6

and for four runners, sample space size = 4!=24

Leave it to you to figure out the appropriate choice.