# 3 students are selected from a class that has 10 boys and 5 girls. What is the probability that 1 boy and 2 girls are selected?

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### 2 Answers

The class has 10 boys and 5 girls. In all there are 15 students.

The number of ways in which 3 students can be selected is 3C15

=> 15! / 3!*12!

=> 455

The number of ways that those selected are 1 boy and 2 girls is 2C5*1C10

=> 5!/2!*3! * 10!/1!*9!

=> 100

The probability is the ratio of the desired events to the total number of events possible.

This is 100/455

**The probability that of the 3 students selected 1 is a boy and 2 are girls is 100/455**

The class has 15 students of which 10 are boys and 5 are girls. Three students are selected (**at random).**

We further assume that the selection is made by **SRSWOR.**

Total number of ways in which 3 students can be selected from 15 students is 15 C 3 = (15*14*13)/ 3! = **455**.

Again, 1 boy can be selected from 10 boys in 10C1 = 10 ways. Also, 2 girls can be selected from 5 girls in 5C2 = 10 ways. By multiplication principle, the combined event can occur in 10*10 = **100** ways.

By using classical definition of probability, the required probability is 100 / 455 = **20 / 91.**

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