Five distinct boxes labeled 1,2,...,5 contain distinct objects. If box 1 contain

Question

Five distinct boxes labeled 1,2,...,5 contain distinct objects. If box 1 contains 1 object, box 2 contains 2 objects, and in general, box j contains j objects. We are allowed to choose only one object from any box (Order does not matter in the selection for the questions below).

(a) how many ways are there to choose 2 objects from separate boxes?

(b) how many ways are there to choose 3 objects from different boxes?

(c) how many ways are there to choose 5 objects from different boxes?

Any help would be great. Thank you in advance.

Explanation / Answer

(a) how many ways are there to choose 2 objects from separate boxes?

=(((1*(2+3+4+5))+(2*(1+3+4+5))+(3*(1+2+4+5))+(4*(1+2+3+5))+(5*(1+2+3+4)))

=170

(c) how many ways are there to choose 5 objects from different boxes?

5C5 *(1*2*3*4*5)=120

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