How many ways are there to pick a selection of $\$1$ worth of identical pennies, $\$1$ worth of identical nickels, $\$1$ worth of identical dimes if you select a total of $16$ coins?
Soln: At first the quantities threw me off when they provided too much information, but the key word is identical which means I do not have to choose between the elements. That being said I applied the bars and stars method arriving at: $C(16 + 3 – 1, 16) =
C( 16 + 3 – 1, 2)$
but looking at their solution they had: $C(16 + 3 – 1, 16) – C(5 + 3 – 1, 5)$
Is it a possible solution typo? I don't see where or why they subtracted, unless they wanted to ask "how many of a certain amount of coin given that there must be at least of coin X"