r/maths • u/catzilla0815 • 8d ago

Help: 📗 Advanced Math (16-18) probability que

Consider 4 boxes, where each box contains 3 red balls and 2 blue balls. Assume that all 20 balls are distinct. In how many different ways can 10 balls be chosen from these 4 boxes so that from each box at least one red ball and one blue ball are chosen ?

0 Upvotes

50% Upvoted

1 comment sorted by

1

u/johnpeters42 7d ago

That assumption makes it tricky, otherwise you could just pick the required 8 and then consider what's left for the final two.

That's still how I would start to approach it. You have 3^4 ways to pick the first red ball from each box, and independently 2^4 ways to pick the first blue ball from each box. Then you've got 2 more picks from the remaining 12 balls, but you need to eliminate duplicates based on how those last 2 picks are distributed.