A man just bought 4 suits 8 shifts and 12 ties If he selects

A man just bought 4 suits, 8 shifts, and 12 ties. If he selects one suit, one shirt, and one tie at random the next day, how many outfit options does he have? He needs three different shirts for his upcoming business trip. In how many ways can he pick the shirts? If he also needs three ties, in how many ways can he pick three shirts AND three ties? Assume each tic can go with every shirt. Given that P(B) = .48. find the following values. Based on the answers to parts a and b. are events A and B independent? Explain why or why not.

Solution

2.

a)

He has 4*8*12 = 384 options. [answer]

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b)

As the order he picks the shirts does not matter, we use combinations.

He can choose in 8C3 = 56 ways. [answer]

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c)

He can choose 3 ties in 12C3 = 220 ways.

Thus, he can choose 3 shirts and 3 ties in 56*220 = 12320 ways. [ANSWER]

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