$151$ cakes shall be split amongst $3$ people under the condition that no one must have more than $75$. How many combinations are possible?

The solution is $${\binom {3+74-1}{3-1}}$$

which is exactly a combination with replacement. 

I don't understand why the number of cakes can be reduced to $74$. There must be some kind of bijectivity between splitting $151$ cakes and the $74$ I don't see.