How many positive integer solutions satisfy the condition $y_1+y_2+y_3+y_4 < 100$ In preparation for an upcoming test I have come across the following problem and I am looking for some help with it just in case a question of its kind comes up on a evaluation. Thanks!

How many positive integer solutions satisfy the condition:$$y_1+y_2+y_3+y_4 < 100$$


The problem is equivalent to put 4 separator between the 99 inner intervals between the 100 objects in such way that, for example starting from the left


*

*$y_1>1$ first group of objects

*$y_2>1$ second group of objects

*$y_3>1$ third group of objects

*$y_4>1$ fourth group of objects

*$y_5>1$ fifth group of objects


such that $$y_1+y_2+y_3+y_4<100$$
that is
$$\binom{99}{4}$$
