Suppose Anil's mother wants to give 5 whole fruits to Anil from a basket of 7 red apples, 5 white apples and 8 oranges. If in the selected 5 fruits, at least 2 oranges, at least one red apple and at least one white apple must be given, then the number of ways Anil's mother can offer 5 fruits to Anil is \_\_\_\_\_\_\_
Answer: 6860
Solutions · 1
Official solution
Possible splits (Oranges, Red, White) summing to 5 with O≥2, R≥1, W≥1: (2,1,2),(2,2,1),(3,1,1).
\[\binom{8}{2}\binom{7}{1}\binom{5}{2} + \binom{8}{2}\binom{7}{2}\binom{5}{1} + \binom{8}{3}\binom{7}{1}\binom{5}{1}\]
=1960+2940+1960=6860