William W. answered • 09/13/21

Math and science made easy - learn from a retired engineer

When you are picking say 2 jackets out of 3, that is a "combination" because, it doesn't matter what order you pick the jackets in, the two jackets are still the two jackets (doesn't matter if one was picked first).

So the possibilities for jackets is _{3}C_{2} and this is typically something you can type in your calculator to determine. If not, you have to use the equation:

It turns out that _{3}C_{2} = 3. You can easily see this if you just label the jackets as A, B, C. The possible choices are AB, AC, and BC.

The number of possibilities for sleeping bags is _{7}C_{2} and the number of possibilities for packets of food is _{12}C_{9}

Once you get each of those values, just multiply them together to get the total number of possibilities. So:

Total # of ways the trip can be outfitted = (_{3}C_{2})•(_{7}C_{2})•(_{12}C_{9})