Word Problem

Roland2rule wrote:A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 10 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?

A. 20
B. 45
C. 59
D. 90
E. 100

OA is B
Do I really need an equation to solve this? pls I need an expert approach here! Thanks

The condition is to check 1 for every 5 receipts, thus, for 10 customers, the guard will check 2 receipts. Since these two customers can be any two, we'll select them randomly.

The number of different samples of customers = 10C2 = 10.9/1.2 = 45.

I assumed that the 10 customers leave together; if it is not so, five or fewer customers leave at one time, and there is a condition that one for every five customers' receipt must be checked, then the number of different samples of customers = 5C1*5C1 = 5*5 = 25. Since there is no option as 25, we can safely choose option B, 45.

The correct answer: B

Hope this helps!

-Jay
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BTGmoderatorRO wrote:A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 10 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?

A. 20
B. 45
C. 59
D. 90
E. 100

OA is B
Do I really need an equation to solve this? pls I need an expert approach here! Thanks

If 10 customers leave the store, 2 of them will be checked. Therefore, there are 10C2 = (10 x 9)/2 = 45 different samples possible.

Answer: B