We need to form a group of 5 men and 2 women from:

• 7 men 👨👨👨👨👨👨👨
• 3 women 👩👩👩

Step 1: Choose 5 men from 7 👨‍💼

We select 5 men from 7. The number of ways to do this is:

(75)=7×62×1=21\binom{7}{5} = \frac{7 \times 6}{2 \times 1} = 21(57​)=2×17×6​=21

So, there are 21 ways to pick the men. ✅

Step 2: Choose 2 women from 3 👩‍💼

Now, we pick 2 women from 3:

(32)=3×22×1=3\binom{3}{2} = \frac{3 \times 2}{2 \times 1} = 3(23​)=2×13×2​=3

So, there are 3 ways to pick the women. ✅

Step 3: Multiply both choices ✖️

Since both choices are independent, we multiply them:

21×3=6321 \times 3 = 6321×3=63

🎯 Final Answer:

The group can be made in 63 ways! 🎊