Question 864326
y1, ..., y5 are positive integers, so the problem is equivalent to finding # of non-negative integer solutions to *[tex \large y_1 + y_2 + y_3 + y_4 + y_5 \le 3]


This is also equivalent to finding the # of solutions to *[tex \large y_1 + y_2 + y_3 + y_4 + y_5 + z = 3], where z is a positive integer (see why?). This is also equivalent to the # of solutions in non-negative integers to *[tex \large y_1 + y_2 + y_3 + y_4 + y_5 + z = 2], which is *[tex \large {7 \choose 2} = 21].


I don't tutor privately here, but there is a list of tutors on algebra.com and I am sure you can arrange with one via email.