Math511Exam1Solutions

# Suppose that 20 marbles are randomly placed into 9

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Unformatted text preview: of the time. Suppose she throws 20 darts at the target. What is the probability that she hits the target exactly 5 times? Solution: This is a binomial experiment with n = 20, p = 0.7, ⎛ 20 ⎞ So the answer is ⎜ ⎟ (0.7 )5 (0.3)15 . ⎝ 5⎠ (b). How many permutations of the 9 letters 1, 2, 3, 4, 5, 6, 7, 8, 9 have 1, 2, 3, 4 appearing in a block together in some order? Examples: 683241975 985213476 123478659 689431257 Solution: Answer: 4 ! × 6! First choose some ordering for the block containing 1, 2, 3, 4 – this can be done in 4!...
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