Question

Five different types of ice-creams and six different types of fruits are available to make a Blizzard. The Blizzard will contain 3 types of ice-creams and 2 types of fruit. How many different Blizzards can be made if green tea flavor (i.e one type of ice-cream) or mango (i.e on type of fruit) or both green tea flavor and mango must be served for the Blizzard? Five different types of ice-creams and six different types of fruits are available to make a Blizzard. The Blizzard will contain 3 types of ice-creams and 2 types of fruit

Answer 1

(a) 18 types of Blizzard have green tea flavor

(b) 20 types of Blizzard have mango

(c) 6 types of Blizzard have green tea flavor and mango

Explanation:

Five different types of ice-creams and six different types of fruits are available to make a Blizzard.

The Blizzard will contain 3 types of ice-creams and 2 types of fruit.

Then the Blizzard can have combinations of 3 types of ice-cream out of 5 posibilities. The amount of combinations is

`C(3oo5)=(n!)/(k!(n-k)!)=(5!)/(3!2!)=10`

For the fruits, we can have combinations of 2 fruits, out of 3 types of fruits.

The amount of combinations is

`C(2oo3)=(n!)/(k!(n-k)!)=(3!)/(2!1!)=3`

The blizzard have 10*3=30 possible combinations.

If one of the ice-creams is defined (green tea flavor), it becomes a combination of 2 in 4 options for the ice-creams (fruit combinations remain the same)

C(2oo4)=\frac{n!}{k!(n-k)!}=\frac{4!}{2!2!}=6

There are 6*3=18 combinations of Blizzard that have green tea flavor.

If one of the fruits is mango, it becomes 1 out of 2 options for the fruits, so we have 2*10=20 combinations of Blizzards that have mango.

If the blizzard have green tea flavor and mango, there are 6*2=12 possible combinations of Blizzard that have this two.