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Question

Ian gave each of his 2 buddies a candy at his birthday celebration, with the treats being 2 Hazel Nut bars, 2 Coconut Milk bars, and 1 Dates bars. What is the probability that both of Ian's friends got the same type of candy?

A
15
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B
25
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C
110
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D
45
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Solution

The correct option is A 15
Given that:

Total number of candy =5

Number Hazel nut bars =2

Number of Coconut milk bars =2

Number of Dates milk bar =1

So,
ways of seletion of 2 Hazel nut bars
=2C2=1

ways of seletion of 2 Coconut milk bars
=2C2=1

and ways of selection 2 candy out 5
=5C2=5×42!=10

Probabilty of getting same Hazel nut bars
=110

Probabilty of getting same Coconut milk bars
=110

Hence,
Probability of getting same type of candy =110+110
=210
=15

Short cut method
There are 2 ways he can give same type of candy to both friends either Hazel nut bars or Coconut milk bars.

And there are 10 ways to select 2 candies out of 5.

So,
Probabilty of getting same type of candy =210
=15

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