Some customers of a retail chain have a store credit card that earns them bonus gifts when they make purchases at the chain. Currently, 22 customers are shopping in a store in this chain. Of these, half already have a store credit card. If employees offer store credit cards to 5 of these, what is the probability that all of those chosen already have a card?
(b) A family of 5 is shopping in the store. Noting that Subscript n Baseline Upper C Subscript xnCx gives the number of ways of picking a subset of x items out of n, what is the probability that the 5 randomly selected shoppers are in this family?
(c) How many possible subsets of those already having a card might the employees select?
d) Combine your answers to (b) and (c) to find the probability that all 5 of those offered credit already have a card.
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