Question

Eleven people, 7 men and 4 women, successfully completed their study at the School of Astronautics. A team of 6 people needs to be selected from them for the next intergalactic travel. In how many ways can 6 astronauts be selected, if at least 2 women and 3 men must be in the team？

thank u!!

Answer 1

For at least 2 women and 3 men, the only cases would be
2W,4M = C(4,2) x C(7,4) = 6x35 = 210 , or
3W,3M = C(4,3) x C(7,3) = 4x35 = 140

for a total of 350 ways

(all possible ways would be
0W,6M
1W,5M
2W,4M
3W,3M
4W 2M )

Answer 2

Worked out combination of women and men
Either 3 women and 3 men or 4 men and 2 women
Then comination for the 2 Women was n = 4 no. of combos was 6 and r = 2 and for the 3 women n = 4 and r = 3 no. of combos was 4

Follow the formula n!/(n-r)! x (r!)

Same process for men. In each instance 35 combinations for Men.

Then times combination for each set which was (6 x 35) + (4 x 35) = 350

350 combinations for the team