Answer:
The probability is 0.2727
Step-by-step explanation:
There are nCk combinations or ways to take k elements from a group of n elements. So, nCk is calculated as:
[tex]nCk=\frac{n!}{k!(n-k)!}[/tex]
Then, there are 66 ways to select two socks from the 12 that are in the basket. This is calculated as:
[tex]12C2=\frac{12!}{2!(12-2)!}=66[/tex]
Additionally, if the student match the socks, he have 3 possibilities:
1. He match socks type A
2. He match socks type B
3. He match socks type C
There are 6 ways to match socks type A, 6 ways to match socks type B and 6 ways to match socks type C. This is calculated as:
[tex]4C2=\frac{4!}{2!(4-2)!}=6[/tex]
Because the student should select 2 socks type A from the 4 socks type A that are in the basket and it is the same calculation for socks type B and Type C.
Finally, there are 18 possibilities to match the socks, so the probability is calculated as:
[tex]P=\frac{6+6+6}{66}=\frac{18}{66}=0.2727[/tex]