Jason L. answered • 01/20/17

Graduate Student Who Loves to Do Math

I'll admit that I'm not sure about the first one, but I can definitely help you on the last two and then maybe someone else will be kind enough to help you on the first.

2) This is asking for the number of combinations of 2 items from the group of 7. Note that it's combinations and not permutations since order does not matter (i.e. a group of milk & cake is the same thing as cake & milk; keep this is mind for part 3).

7C2

=7!/(2! * 5!)

= 7 * 6 / 2

=21

3) This one is asking for the number of permutations since order does matter (i.e. if Tom is President and Jerry is VP, then that is not the same thing as Jerry as President and Tom as VP). While it may seem intuitive to think you are picking permutations of 5 from your group of 100, since Tom has to have a spot guaranteed we are actually picking 4 out of 99.

99P4

= 99!/95!

= 90,345,024

However, we are still not done here. That 90 million number is the number of perms of the other 99 cats, but we also have to account for the fact that Tom could be in any of the 5 cabinet spots. So the final answer is actually:

5P1 * 99P4

= 5 * 90,345,024

= 451,725,120

Ellen B.

01/20/17