Question

How many different teams of 3 can be chosen from a group of 11 adults and 15 children if each team must have at least one adult on it?

Answer 1

How many different teams of 3 can be chosen from a group of 11 adults and 15 children if each team must have at least one adult on it?

In this case: for “no adults” there are ways =  “15 C 3” = 15! / (12! * 3!) = (15*14*13)6 = 455

The total number, with adults or not is:
“11+15 = 26 C 3 = 26! / (23! * 3!) = 26*25*24/6 = 2600

Then:
Number of teams with “At least one adults” =vTotal Number of teams - Number of teams with “no adults” = 2600 - 455= 2145