In how many ways can we select five coins from a collection of 10 consisting of one penny, one nickel, one dime, one quarter, one half-dollar and 5 (IDENTICAL) Dollars ?
For my answer, I used the logic, how many dollars are there in the 5 we choose?
I added the case for 5 dollars, 4 dollars, 3 dollars and 2 dollars and 1 dollars and 0 dollars. $$C(5,5) + C(5,4) + C(5,3) + C(5,2) + C(5,1) + 1 = 32$$
which is the right answer ... but there has to be a shorter way, simpler way. I tried using the repetition formula that didn't pan out.
If you could introduce me to a shorter way with explanation I appreciate it.