### Permutation Combination Question 6

#### Question 6 - 25 January - Shift 2

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 orange, 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 __________

## Show Answer

#### Answer: 6860

#### Solution:

#### Formula: Combinations of Alike Objects

7 Red apple(RA), 5 white apple(WA), 8 oranges (O)

5 fruits to be selected (Note:- fruits taken different)

Possible selections :- (2 O, 1 RA, 2 WA) or (2 O ,2 RA, 1 WA) or (3 O, 1 RA, 1 WA)

$\Rightarrow{ }^{8} C_2 { }^{7}C_1{ }^{5} C_2+{ }^{8} C_2{ }^{7} C_2{ }^{5} C_1+{ }^{8} C_3{ }^{7} C_1{ }^{5} C_1$

$= 1960+2940+1960$

$= 6860$