I could solve it in arround 10 min. basically totally there are 15 (10 men + 5 women as mentioned)member out of that 12 chosen then toal ways 15c12. now to get atleast 2/3 of member it means total men selected in group should be 8 or 9 or 10(why 10- as total to men are only there), total ways - 10c8...