Question

An interior decorator must furnish two offices. Each office must have a desk, a chair, a file cabinet and 2 bookcases. At the local office furniture store there are 6 models of desks, 8 models of chairs, 4 models of file cabinets and 10 models of bookcases, all of which are compatible. (Any desk can be matched with any chair, etc.) How many choices does the decorator have if he wants to select two desks, two chairs, two file cabinets and four bookcases if he doesn't want to select more than one of any model?

Answer 1

He has 101,606,400 options.

Explanation:

The decorator wants to select 2 desks. He has 6 models to select from and he doesn't want to select more than one of any model (therefore his choices are without replacement). So for the first desk he will have 6 options and for the second one he will have 5 options. 6 x 5 = 30 options.

Following the same procedure for the 2 chairs, he has: 8 x 7 = 56 options.

Now, for the two cabinets: 4 x 3 = 12

And for the bookcases = 10 x 9 x 8 x 7 = 5040

Now we are going to multiply all these options (because he has two select two desks AND two chairs AND two cabinets AND four bookcases:

30 x 56 x 12 x 5040 = 101,606,400