Barney Stinson from How I Met Your Mother is trying to decide what to wear befor

Question

Barney Stinson from How I Met Your Mother is trying to decide what to wear before heading to MacLaren's. He has three suits (gray, black, and navy blue), two ties (solid and pattern), and five dress shirts (white, black, blue, red, and green) to choose from. a) How many days could he go before he would have to repeat the exact same outfit? b) What is the probability that a randomly selected outfit will consist of the navy blue suit? c) Labor Day is not far away, and there is an old rule that says you can no longer wear white after it. Therefore, Barney wants to capitalize on the time he has remaining by only wearing the white dress shirt. How many outfits can he create now?

Explanation / Answer

3 suits , 2 ties and 5 dress shirts

a)

no of possible combinations = 3*2*5 = 30

so no of days could he go before he would have to repeat the exact same outfit = 30

b)

no of possible outfits with navy blue suit = 1*2*5 = 10

probability that a randomly selected outfit will consist of the navy blue suit = 10/30 = 1/3 = 0.33

c)

no of outfits with white dress shirt = 3*2*1 = 6

i.e he can create 6 outfits by wearing white dress shirt

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