Splitting a 75 million fund across five asset classes

A fund holds $75 million, all of which must be invested across five asset classes: equity options, commodity futures, fixed income, event contracts and cryptocurrencies. Allocations are made in whole multiples of $1 million, and an asset class may receive nothing. (For instance, $7M, $35M, $20M, $12M and $1M respectively would be one valid allocation.)

(a) How many distinct allocations are possible?

(b) How many are possible if every asset class must receive at least $5 million?

(a) $\binom{79}{4}=1{,}502{,}501$; (b) $\binom{54}{4}=316{,}251$. Treat each $1M as a star and separate the five classes with four bars, so you are choosing where the 4 bars go among $79$ symbols. For (b), hand out $5M to every class first, then distribute the remaining $50M freely: $\binom{54}{4}$.