# Probability and Combinatorics problem?

There are 8 students in a class: 2 boys and 6 girls.

If the teacher picks a group of 5 at random, what is the probability that everyone in the group is a girl?

I need some idea for this problem.

### 3 respuestas

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• Respuesta preferida

If a group of 5 contains all girls then there are no boys.

so, girls => 6C5 = 6

Boys => 2C0 = 1

so, 5 girls and 0 boys => 6 x 1 = 6

Total choices => 8C5 = 56

Hence, 6/56 = 3/28

:)>

• Use the formula for the number of combinations of n things taken k at a time.

Since the picking is random, every combination has the same probability. So all you have to do is get the counts.

The answer is the number of ways to choose 5 of the 6 girls, divided by the number of ways to choose 5 of the 8 students.

• for the first pick, prob. is 6/8

for next 4: 5/7, 4/6, 3/5, 2/4

multiply them together to get overall probability

(6/8)(5/7)(4/6)(3/5)(2/4)

(3/4)(5/7)(2/3)(3/5)(1/2)

(3/4)(1/7)(1/1)(1/1)(1/1)

3/28

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