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A grocery store is running a promotion that you will get one card from 6 different...

A grocery store is running a promotion that you will get one card from 6 different colored cards every time you shop there. And a customer who collects all 6 types of cards(one of each color) will win $100 gift card. Assume that the cards are distributed evenly. How many times minimum a customer has to shop there to be sure to win a $100 gift card?

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Answer #1

Minimum number of times a customer has to shop there to be sure to win a $100 gift card is 6 times, because of the following reason:

Let the 6 colors be A, B, C, D, E and F.

First time: It can be any of the 6 colors: say Color A

Second time: By luck, it may be any of the other 5 colors: say, Color B

Third time, By luck, it may be any of the other 4 colors: say, Color C

Fourth time, By luck, it may be any of the other 3 colors: say, Color D

Fifth time, By luck, it may be any of the other 2 colors: say, Color E

Sixth time, By luck, it may be any of the other 1 color: Color F

Thus, answer is:

6

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