Respuesta :
Answer:
(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
Step-by-step 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
[tex]C(3oo5)=\frac{n!}{k!(n-k)!}=\frac{5!}{3!2!}=10[/tex]
For the fruits, we can have combinations of 2 fruits, out of 3 types of fruits.
The amount of combinations is
[tex]C(2oo3)=\frac{n!}{k!(n-k)!}=\frac{3!}{2!1!}=3[/tex]
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.
