# 6.5 WorksheetExercise 6.5.5: Choosing a chorus.(a) There are 30 boys and 35 girls that try out for a chorus. The choir director will select 10 girls and 10 boysfrom the children trying out. How many ways are there for the choir director to make his selection?Exercise 6.5.6: Counting possible computer failures.Suppose a network has 40 computers of which 5 fail.(a) How many possibilities are there for the five that fail?(b) Suppose that 3 of the computers in the network have a copy of a particular file. How many sets of failureswipe out all the copies of the file? That is, how many 5-subsets contain the three computers that have the file?Exercise 6.5.7: Choosing a student committee.bo uol14 students have volunteered for a committee. Eight of them are seniors and six of them are juniors.(a) How many ways are there to select a committee of 5 students?GGUdnaund us ieinoo(b) How many ways are there to select a committee with 3 seniors and 2 juniors?veling(c) Suppose the committee must have five students (either juniors or seniors) and that one of the five must beselected as chair. How many ways are there to make the selection?Page 3 of 4 6.5 WorksheetExercise 6.5.8: Counting five-card poker hands.This question refers to a standard deck of playing cards. If you are unfamiliar with playing cards, there is anexplanation in "Probability of an event" section under the heading "Standard playing cards." A five-card handis just a subset of 5 cards from a deck of 52 cards.(a) How many different five-card hands are there from a standard deck of 52 playing cards?(b) How many five-card hands have exactly two hearts?(c) How many five-card hands are made entirely of hearts and diamonds?(d) How many five-card hands have four cards of the same rank?ebutaEXE(e) A "full house" is a five-card hand that has two cards of the same rank and three cards of the same rank.For example, {queen of hearts, queen of spades, 8 of diamonds, 8 of spades, 8 of clubs}. How many five-cardhands contain a full house?diw sotiimm0 oolo(f) How many five-card hands do not have any two cards of the same rank?

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6.5.5) It is given that there are 30 boys and 35 girls. The choir director will ...

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