Empty Basket(s)
Probability
Level
pending
How many ways can you place 10 identical balls in 3 baskets of different colors if it is possible for a basket to be empty?
The answer is 66.
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1 solution
In this case the balls are identical. So we do not have to worry about which ball is going into which basket but what number of balls is kept in each basket. Let the number of balls in first basket be X , in second basket be Y,and in third basket be Z . Hence
X+Y+Z=10. So the number of ways we can keep the balls in the baskets by obeying the condition that a basket can be empty is the number of non negative integral solution of the above equation and that's equal to 12C2=66.