Daily Tech Puzzle #14
Sponsored by MindSumo

Ahh summer. Picnic time. So you're packing a small picnic for yourself and two friends and you're prepping 3 bags total.

Each bag should consist of three types of fruit. You went ahead wrapped up each of the 9 fruits you plan to pack into little boxes and sealed them. They are now indistinguishable from one another.

You put three little boxes into each bag (i.e. 3 indistinguishable boxes of fruit per bag, 3 bags total).

If the probability that each guest got one fruit of each type is m / n, where m and n are relatively prime integers, what is m+n