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?
← JEE Advanced 2022 · Paper 2
MathematicsSingle correct+3 / -1Question 15 of 54
JEE Advanced 2022 · Paper 2, Mathematics question 15
Answer and worked solution
Official answer: A
Ways to take balls from one box (3 red, 2 blue) with at least one of each colour:
- : .
- : (remove the all-red choice).
- : (four balls always include both colours).
Split the 10 balls. Each box gives at least 2, which leaves 2 extra.
- One box takes 4: .
- Two boxes take 3: .
Total. . (A).