How many ways are there to appoint 6 diplomats ten adorian and fifteen tellartie diplomats are available for a treaty delegation. the question :10 Adorian and 15 Tellarite diplomats are available for a treaty delegation. How many ways are there to appoint six diplomats to the delegation if there must be the same number of Andorians and Tellarite? WHat I did was: I use the repetition permutations and there's no answer on this question please help.

Since you're forming a six-person delegation, the only way both sides will be equal is if there are $3$ Adorians and $3$ Tellarites. (Repetition isn't appropriate here because one person can't be on the delegation twice).

Number of ways to choose $3$ Adorians = $\binom{10}{3}$.

Number of ways to choose $3$ Tellarites = $\binom{15}{3}$.

Since these are independent options, we multiply them together to get

$$\binom{10}{3}\binom{15}{3}$$