6.5 Worksheet Exercise 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 boys from 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 failures wipe 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 uol 14 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? GGU d naund 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 be selected as chair. How many ways are there to make the selection? Page 3 of 4 6.5 Worksheet Exercise 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 an explanation in "Probability of an event" section under the heading "Standard playing cards." A five-card hand is 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?ebuta EXE (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-card hands contain a full house? diw sotiimm0 oolo (f) How many five-card hands do not have any two cards of the same rank?