how do i solve this probabiltiy problem

Question

4C1 . 6C3

       10C4

 

 

Answer 1

ncr = n! / (n - r)! * r!

4c1 = 4! / (4-1)! * 1! = (4 * 3!) / 3! * 1 = 4

6c3 = 6! / (6-3)! * 3! = (6 * 5 * 4 * 3!) / 3! * 3! = 120 / 6 = 20

10c4 = 10! / (10-4)! * 4! = (10 * 9 * 8 * 7 * 6!) / 6! * 4! = 5040 / 24 = 210

4c1 * 6c3 / 10 c4 = (4 * 20 ) / 210 = 80 / 210 = 8/21