easy Probability

Team Split

A release-checked easy problem for training Combinations and Permutations.

Question

There are $15$ people that need to be split up into three teams $-$ the quant team, which needs $6$ people, the trading team, which needs $3$ people, and the engineering team, which needs $6$ people. Three of the people $-$ Lewis, Lilly, and Scotty $-$ don't know how to code and thus can't be put on the engineering team. How many different ways can teams be formed?

Practice focus

This Probability problem is tagged Combinations and Permutations. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.