Given:Total number of men = 7Total number of women = 6The total number of people need to select = 5The total number of men will be in the final team = 3Formula used:The number of ways of selecting r things out of n = nCrAlso, nCr = \(\frac{n!}{r!×(n-r)!}\)Calculation:According to the question, we may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only)The required number of ways to select 3 men and 2 women = 7C3 × 6C2? \(\frac{7!}{3!×(7-3)!} × \frac{6!}{2!×(6-2)!}\)? \(\frac{(7\times 6\times 5)}{(3\times2\times1)}\)×\(\frac{(6\times 5)}{(2\times1)}\)? 35 × 15? 525The required number of ways to select 4 men and 1 woman = 7C4 × 6C1? \(\frac{7!}{4!×(7-4)!} × \frac{6!}{1!×(6-1)!}\)? \(\frac{(7\times 6\times 5)}{(3\times2\times1)}\)× 6? 35 × 6? 210The required number of ways to select 5 men only = 7C5? \(\frac{7!}{5! × (7-5)!}\)? (7 × 6)/(2 × 1) = 21? Total number of ways = 525 + 210 + 21 = 756?? The people can be selected in a total of 756 ways.