Question

there are 4 men and 5 women. find the number of ways of selecting 3 of which atmost one women

Answer 1

Hey.....!!! here is ur answer........☺️☺️☺️

We can choose by following type........

(4C1×5C2)/9C3 + (4C2×5C1)/9C3.........(1).....,
where "C" belongs to Combination

We know that nCr = n!/r!(n–r)!

Then, 4C1 = 4!/1!(4–1)! = 4.3!/3! = 4

Such that, 5C2 = 5!/2!.3! = 5.4/2.1 = 10

4C2 = 4!/2!.2! = 4.3/2.1 = 6

5C1 = 5!/1!.4! = 5

and 9C3 = 9!/3!.6! = 9.8.7/3.2.1 = 84

On putting all these value in equation (1).

=>(4×10)/84 + (6×5)/84

=>40/84 + 30/84

=>70/84

=>5/6 ««««««Ans.

I hope it will help you.........✌️✌️✌️