Suppose we have seven identical balls to be distributed in bins labeled A, B, C, and D....

Suppose we have seven identical balls to be distributed in bins labeled A, B, C, and D. For example, one way to distribute the balls is to place two in A, none in B, four in C, and one in D.

a) How many ways are there to distribute the balls among the four bins? Explain your answer.

b) How many ways are there to distribute the balls so that at each bin has at least one ball in it? Explain your answer.

c) How many ways are there to distribute the balls so that at least one of the bins is empty? Explain your answer.

d) How many solutions are there to the equation a + b + c + d = 7, where a, b, c, and d must be positive integers? Explain your answer.

Expert Solution

I wrote the generalised explanation for distribution of n identical objects to r different places in 1st page

orchestra answered 1 year ago

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