I have a hat that contains six nickels and five pennies. I draw coins from the hat at random, without replacement. Find the probability that after drawing four coins, I have removed at most two pennies from the hat.

37/66

Step-by-step explanation:

To have removed at most 2 pennies out of 4 coins, you could have either selected 4 nickels, 3 nickels, and 1 penny or 2 nickels and 2 pennies.

There is only one way to select 4 nickels:  6/11 x 5/10 x 4/9 x 3/8  =  1/22

There are four ways to select 3 nickels and 1 penny; each way is:  6/11 x 5/10 x 4/9 x 5/8  =  1/66

    4 x 1/66  =  2/33

There are six ways to select 2 nickels and 2 pennies; each way is:  6/11 x 5/10 x 5/9 x 4/8  =   5/66

    6 x 5/66  =  5/11

Adding these probabilities:  1/22 + 2/33 + 5/11  =  37/66

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