1. In how many ways can 30 identical balls be distributed into 7 distinct boxes (numbered "Box 1, Box 2, ..., Box 7") subject to the following conditions?

(a) With no constraints.

(b) Each box gets at least three balls.

(c) Each of the odd-numbered boxes gets exactly one ball, and each of the even-numbered boxes gets at least one ball.

(d) Each box gets an even number of balls.

For the 1st one i get 36C6 is this correct?

(a) With no constraints.

(b) Each box gets at least three balls.

(c) Each of the odd-numbered boxes gets exactly one ball, and each of the even-numbered boxes gets at least one ball.

(d) Each box gets an even number of balls.

For the 1st one i get 36C6 is this correct?

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