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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?

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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

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

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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