8) Answer the following: a) If n(B)-30, n(AUB)-60 and n(AnB)-10, what is n(A)? b

Question

8) Answer the following: a) If n(B)-30, n(AUB)-60 and n(AnB)-10, what is n(A)? b) S {Barnsley,Manchester United,Southend, Liverpool, Lyon, Royal Tiger) Let A=(Southend, Liverpool,Royal Tiger) Let B-(Manchester United,Southend, Liverpool) What is n[(AnB)' ]? c) How many six-letter sequences are possible that use the letters ff.,a.a.ff. d) Miss K has a bag of marbles. The bag contains 3 yellow marbles, 5 red marbles and 4 blue marbles. Miss K reaches into her bag and randomly pulls out three marbles. How many ways can she get at leasy one yellow marble? How many ways can she get at exactly one of each color?

Explanation / Answer

a) n(A U B) = n(A) + n(B) - n(A B)

or, 60 = n(A) + 30 - 10

or, n(A) = 40

b) A B = {southend, liverpool}

n[(A B)'] = 1 - n(A B) = 6 - 2 = 4

c) Number of different sequences = 6! / (4! * 2!) = 15

d) total marbles = 3 + 5 + 4 = 12

Number of ways to select at least one yellow = Total number of ways to select 3 marbles - total number of ways to select zero yellow marbles

                                           = 12C3 - 9C3

                                           = 220 - 84

                                           = 136

Number of ways to get one of each color = 3C1 * 5C1 * 4C1 = 3 * 5 * 4 = 60

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