Question

In how many ways can 10 men be divided into two groups of 4 men and 6 men?

• A. 5040
• B. 151200
• C. 210
• D. 2520

Hint:

To find the number of ways to divide a group into smaller groups, use combinations and ensure that the total number of men adds up to the original group size.

Answer 1

The Correct Option is C

Step 1: Number of Ways to Select 4 Men from 10.
The number of ways to select 4 men from 10 is given by the combination formula: \[ C(n, r) = \frac{n!}{r!(n - r)!} \] Substituting \( n = 10 \) and \( r = 4 \): \[ C(10, 4) = \frac{10!}{4!(10 - 4)!} = \frac{10 \times 9 \times 8 \times 7}{4 \times 3 \times 2 \times 1} = 210 \]

Step 2: Conclusion.
Thus, the number of ways to divide the 10 men into two groups of 4 and 6 is 210.

Final Answer: \[ \boxed{210} \]