A certain club contains 10 men and 10 women. a six-member committee consisting of 2 men and 4 women must be chosen from the club. how many committees are possible

Out of the men the number of ways you can choose 2 is 10C2 = (10*9) / (2*1)

= 45 ways

out of the women number of ways = 10C4 = (10*9*8*7) / (4*3*2*1)

= 210 ways

So the number of committees possible = 45 * 210 = 9450.