Question

Can you help me understand how to do this ?

Answer 1

2/9

Step-by-step explanation:

The number of ways to select x people from a group of n people is calculated as

`\text{nCx}=(n!)/(x!(n-x)!)`

Then, the number of ways to select 2 people from a group of 10 is:

`10C2=(10!)/(2!(10-2)!)=(10!)/(2!\cdot8!)=45`

So, there are 45 different ways to select two people.

On the other hand, the number of ways to select 2 boys is equal to

`5C2=(5!)/(2!(5-2)!)=(5!)/(2!\cdot3!)=10`

Because there are 5 boys.

Then, the probability that the teacher will chosse two boys is:

`P=(10)/(45)=(2)/(9)`

Therefore, the answer is 2/9