Week 15 - Quiz: seeking explanation for an answer

For this question:
out of 126 students, two study group of 48 and 78 students are formed by random sampling. If you and one of your best friends are part of this study group, what is the probability that both of you will end up in the same group?

The answer is
Both in the group of 48 students: 124C46/126C48
+
Both in the group of 78 students: 124C76/126C76.

I understand the denominator part, you are choosing 48 students out of 126 in total and 78 students out of 126 in total for each group. Can someone please explain why is the numerator 124C46 and 124C76?

Hi @magesh.ramasamy,
To get the number of favorable outcomes, you’ll have to assume you and your friend are in the same group.
In such a case, you can only choose between 124 other students, which excludes out you and your friend.
I hope this helps.