Permutation.

A bag contains 2 apples, 3 oranges, and 4 bananas. The number of ways in which 3 fruits can be selected if atleast one banana is always in the combination (Assume fruits of same species to be alike) is

Expert Solution

We have to select 3 fruits. It will contain 1 banana and 2 more fruits.

Case 1: 2 fruits are bananas.

Number of ways = 1

Case 2: both are not bananas

a) both are same fruits

Number of ways = ²C1 = 2

b) both are different fruits

Number of ways = 1

Case 3: 1 fruit is banana

Number of ways = 1×²C1 = 2

total number of ways = 1 + 2 + 1 + 2

= 6

Total number of ways =6

Nikhil Thakur answered 2 years ago

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