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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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!...

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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

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