The document discusses a combinatorial problem involving 14 children forming two teams of seven, with a requirement that siblings Andrew, Beth, and Charlie are on the same team. The solution involves calculating the number of ways to split the group while ensuring the siblings are together. The final answer is 275 ways to achieve this formation.

1. Suppose there are 14 children trying to form two teams with seven children each. Andrew, Beth,
and Charlie are siblings and are part of the group. They demand to be on the same team as each
other. How many ways can we split the group of 14 children into two-teams of seven, insuring
that Andrew, Beth, and Charlie are on the same team?
Solution
given 14 children,
(11c4 * 3c3)/ (14c7) * 11c7
=275