From a group of 7 men and 6 women, five persons are to be selected with at least 3 men.
Hence we have the following 3 choices
We can select 5 men ------(Option 1)
Number of ways to do this = ⁷C₅
We can select 4 men and 1 woman ------(Option 2)
Number of ways to do this = ⁷C₄ x ⁶C₁
We can select 3 men and 2 women ------(Option 3)
Number of ways to do this = ⁷C₃ x ⁶C₂
Total number of ways
= ⁷C₅ + [⁷C₄ x ⁶C₁] + [⁷C₃ x ⁶C₂]
= ⁷C₂ + [⁷C₃ x ⁶C₁] + [⁷C₃ x ⁶C₂] [Applied the formula ⁿC_r = ⁿC_{(n - r)} ]

$=\left[\frac{7\times 6}{2\times 1}\right]+\left[\left(\frac{7\times 6\times 5}{3\times 2\times 1}\right)\times 6\right]+\left[\left(\frac{7\times 6\times 5}{3\times 2\times 1}\right)\times \left(\frac{6\times 5}{2\times 1}\right)\right]$

= 21 + 210 + 525 = 756