How many different committees can be formed from 8 teachers and 48 students if the committee consists of 3 teachers and 4 students?

Since we don't care about the order in which we select people, we will use the combinatoric approach, rather than permutations.
Since we want to select 3 teachers from a total of 8, this is the notation to select 3 teachers from 8 (objects).

Teachers :
Similarly, students :

Now, since we want both at the same time, we will need to multiply both to yield your final different ways.

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