How many different committees can be formed from 8 teachers and 32 students if the committee consists of 3 teachers and 4 ​students?

Answer 1

(8 choose 3)(32 choose 4)

(8*7*6/(3*2)) ( 32 * 31 * 30 * 29 / (4*3*2))= <--- 5! and 28! cancels out of both combinations

8*7 * 8 * 31 * 10 * 29 /2 = <---- 6 cancels; 32/4=8; 30/3 = 10

8*7*8*31 * 5 * 29 <--- 10/2 = 5

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