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Three varieties of mangoes and four varieties of apples are available for shakes in a juice centre. More than one mango can be used in one shake but same is not the case with apple. Only one apple can be used in one shake. However, apples and mangoes can also be mixed to make shakes. Find the total number of shakes available in the juice centre.

Three varieties of mangoes and four varieties of apples are available for shakes in a juice centre. More than one mango can be used in one shake but same is not the case with apple. Only one apple can be used in one shake. However, apples and mangoes can also be mixed to make shakes. Find the total number of shakes available in the juice centre. Correct Answer 39

Given:

Three varieties of mangoes and four varieties of apples are available for shakes in a juice centre

More than one mango can be used in one shake but same is not the case with apple

Only one apple can be used in one shake

Apples and mangoes can also be mixed to make shakes

Concept:

To find the total number of ways, first the various cases possible pertinent to the situation has to be finalised. Then, number of ways of arranging in each of the cases possible has to be found out.

Calculation:

Case 1: One Apple is in the shake

Case 2: shake contains only mango

Case 1: One apple can be chosen out of 4 in 4 ways

No Mango can be chosen – 1 way

1 variety of mango can be chosen from 3 different variety = 3C1 = 3

2 varieties of mangoes can be chosen in 3C2 ways = 3

All three varieties can be chosen in 1 way

Total ways = 4 × (1 + 3 + 3 + 1) = 4 × 8 = 32

Case 2: Shake contains only mango

One mango in 3C1 = 3 ways

Two mango in 3C2 = 3 ways

Three mangoes in 3C3 = 1 way

Total ways = 3 + 3 + 1 = 7

∴ Total ways of selecting the shake = 32 + 7 = 39

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