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a) A production lot of 15 television sets contains 3 defective sets. In how many

ID: 3044110 • Letter: A

Question

a) A production lot of 15 television sets contains 3 defective sets. In how many different ways can a hotel purchase five of these sets and receive at least 2 defective sets? (2.5 Points) b) A student club has 40 members and they want to select two officers of the club without replacement. The first person selected will become the president and the second person selected will become the treasurer. If one of the 40 people, say A, says that he will serve only if he is selected as the president, how many different ways the two positions can be filled? (2.5 Points)

Explanation / Answer

Solution:

( a )

Total number of television sets = 15

number of defective sets = 3

number of sets to be purchased = 5

number of ways 5 sets purchase and with 2 defective sets = 3C2 * 12C3 = 3 *220 = 660

number of ways 5 sets purchase and with 3 defective sets = 3C3 * 12C2 = 1 * 66 = 66

number of ways 5 sets purchase and with atleast 2 defective sets = 660 + 66 = 726

( b )

Total members in the club = 40

Given, one person A said he will serve only as a president

therefore,

number of ways of selecting A as president and another treasurer = 1 * 39 = 39

number of ways of not selecting A as president and another treasurer = 39 * 38 = 1482

total number of ways of selecting a president and a treasurer = 39 + 1482 = 1521