There are 7 students in a class: 2 boys and 5 girls.
If the teacher picks a group of 3 at random, what is the probability that everyone in the group is a girl?

Step-by-step explanation:

There are

7

students in a class,

5

boys and

2

girls.

If the teacher picks a group of

4

at random, what is the probability that everyone in the group is a boy?

Probability:

The probability of choosing

a

boys from a group of

n

students is given by

a

n

. If the number of boys to be chosen are less than

a

let's say

r

, we will have to consider all possible ways to select

r

boys from

a

. So the expression to calculate the probability becomes...

a

C

r

n

C

r

=

(

a

r

)

(

n

r

)

Answer and Explanation:

The probability that everyone in the group is a boy is given by

5

C

4

7

C

4

=

(

5

4

)

(

7

4

)

=

5

×

4

×

3

×

2

×

1

7

×

6

×

5

×

4

=

1

7

44

step-by-step explanation:

the