kitchen table math, the sequel: how many different groups of 4?

## Wednesday, March 2, 2011

### how many different groups of 4?

A school librarian would like to buy subscriptions to 7 new magazines. His budget, however, will allow him to buy only 4 new subscriptions. How many different groups of 4 magazines can he choose?

Daniel Ethier said...

There are four slots, with 7 choices for slot 1, 6 for slot 2, 5, for slot 3, and 4 for slot 4. But order does not matter. You either subscribe or you don't. So we need to divide by the number of ways to arrange the four subscriptions, which is 4 x 3 x 2 x 1. Much canceling ensues, leaving 7 x 5 on top for 35 possible subscriptions.

Doug Sundseth said...

A slightly easier way to get to the same answer is to realize that choosing 4 out of 7 means not choosing 3 out of seven. Following the same pattern, there are 7 subs to reject in the first slot, 6 in the second, and 5 in the third. Order doesn't matter, which means:

7x6x5/1x2x3 = 35.

This is pretty trivially different here, but in some cases, the problem can be much simplified:

How many ways are there to choose 25 out of 27, for instance:

27*26/1*2 is quite a bit easier than the alternative, if only because it requires less writing.

Catherine Johnson said...

Doug!

Hi!!!!!