xander spends most of his time with his 10 closest friends. he has known 4 of his 10 friends since…

Explanation:

Step1: Calculate first - friend probability

The probability that the first friend to show up is a friend known since kindergarten is $\frac{4}{10}$ because there are 4 such friends out of 10 total friends.

Step2: Calculate second - friend probability

After one friend known since kindergarten shows up, there are 3 friends known since kindergarten left out of 9 remaining friends. So the probability that the second friend to show up is also a friend known since kindergarten is $\frac{3}{9}$.

Step3: Calculate third - friend probability

After two friends known since kindergarten show up, there are 6 non - kindergarten - known friends out of 8 remaining friends. So the probability that the third friend to show up is not a friend known since kindergarten is $\frac{6}{8}$.

Step4: Calculate overall probability

We multiply the probabilities of each step together: $\frac{4}{10}\times\frac{3}{9}\times\frac{6}{8}=\frac{4\times3\times6}{10\times9\times8}=\frac{72}{720}=\frac{1}{10}$.

Answer:

$\frac{1}{10}$