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You have 30 of each of the following type of objects: A, B, C, and D. The objects of each type ar...

You have 30 of each of the following type of objects: A, B, C, and D. The objects of each type are identical. In how many ways can you choose a set S of 80 objects? (Each type is identical so it isn't just 120 C 80).

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Answer #1

Let n1, n2, n3 and n4 be the number of objects selected of Type A, B, C and D respectively.

Hence, we have, n1 + n2 + n3 + n4 = 80, where, 0 <= n1, n2, n3, n4 <= 30.

Thus, the number of ways we can choose 80 objects =

30 t130min (30,80-n1-n2min (30,80-n1-n2-n330 130 2 rlmin(30,80 - nl - n2) 7lmin(30,80 - nl - n2 n3) n4, where, n1 + n2 + n3 + n4 = 80. (Ans).

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