Question

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 ofter 5 fruits to Anil is______

Answer 1

The correct answer is 6860
7 Red apple(RA),5 white apple(WA), 8 oranges (O)
5 fruits to be selected (Note:- fruits taken different)
Possible selections :- (2O,1RA,2WA) or (2O,
2RA,1WA) or (3O,1RA,1WA)
⇒8C2​7C1​5C2​+8C2​7C2​5C1​+8C3​7C1​5C1​
⇒1960+2940+1960
⇒6860