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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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