Cosmin has three ping pong balls, and ten cups in front of him. If he throws the ping pong balls into the cups, what is the probability that exactly two balls land in the same cup? (A ping pong ball has an equal probability of landing in any cup.)

 Nov 29, 2020

Let the balls be Red Blue and Yellow.  My method requires that the ball be thought of as different

the pairs are   RB, RY and BY  so there  are 3 ways to pair them.


Number of ways the balls can go into the cups is 10*10*10 = 1000


Number of ways to get Blue and Red together and Yellow somewhere else = 10*1*9=90

there are 3 possible pairings    so that is 90*3=270


So P(exactly 2 in the same cup)  = 270/1000 = 27/100



Another way to look at it is by subtraction:

the number of ways they can all be in different cups is 10*9*8 = 720

The number of ways they can all be in the same cup is 10*1*1 =10

so the number of ways that 2 will be in a cup is 1000-720-10 = 270


the answer is the same so that is conclusive enough for me.

 Nov 30, 2020

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