Q5. A real estate agent is showing homes to a prospective buyer. There are twelv
ID: 2921703 • Letter: Q
Question
Q5. A real estate agent is showing homes to a prospective buyer. There are twelve homes in the desired price range listed in the area. The buyer has time to visit only five of them. a. In how many ways could the five homes be chosen if the order of visiting is considered? b. In how many ways could the five homes be chosen if the order is disregarded? c. If eight of the homes are new and four have previously been occupied and if the five homes to visit are randomly chosen, what is the probability that exactly four of the homes to visit are new?Explanation / Answer
a) 12 P5
=12!/(12-5)!
=12!/7!
= 12 *11 *10*9*8
= 95040
b)
12C5
= 12!/(7!*5!)
= 95040/120
= 792
c)
8 new 4 occupied
P(exactly 4 of homes are new)
= 8C4 * 4C1 /12C5
= 70*4 / 792
= 0.353535
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