Question

You and two of your friends are in a group of 10 people. The group is
randomly split up into two groups of 5 people each. Specify an appropriate
sample space and nd the probability that you and your two friends are in
the same group.

Answer 1

The total number of ways that total 10 people could be separated into 2 groups is computed as the number of ways of selecting 5 people from the 10 people.

If the 10 people are labelled as A, B, C, D, E, F, G, H, I and J

Then the sample space here would be given as all the possible combinations of 5 people from them.

Now the probability that I and two of my friends are in the same group is computed here as:

First we compute the number of ways in which me and 2 of my friends are together. The number of ways here would be the number of ways to select the remaining 2 people from the 7 who would be in our group. This is computed as: (7c2) = 21

Therefore now the probability here is computed as: