Question

Suppose sam has 12 black, 3 blue, 4 green, 2 yellow. 2 orange, 6 pink and 7 red chopsticks . How many sticks must he choose so that he is guaranteed a matching pair.

Answer 1

In order to get a matching pair he needs to choose 8 chopsticks.

We know there are 7 chopsticks.

Now there is 7C1 ways to choose the chopstick.

In this case he might or might not get a matching one.

The probability of getting the black chopstick is highest.

While getting the yellow and red one being the lowest.

So if there are n types of chopsticks in order to get a matching pair you need to choose (n+1) chopsticks.

So here one needs to choose (7+1) chopsticks to get a matching pair.