How many different committees can be formed from 88 teachers

How many different committees can be formed from 88 teachers and 3838 students if the committee consists of 22 teachers and 44 students?

Solution

22 teachers are selected in :C(88,22) ways

44 students are selected in :C(3838,44) ways

So total number of different committees are:

C(88,22)C(3838,44)