A committee of 5 is chosen from 10 men and 6 women. Determine the number of ways of selecting the committee if there are no restrictions

To determine the number of ways to select a committee of 5 people from a group of 10 men and 6 women, we use the combination formula. 

### Combination Formula:
The number of ways to choose \( r \) items from a set of \( n \) items is given by the combination formula:

\[
\binom{n}{r} = \frac{n!}{r!(n-r)!}
\]

### Application to the Problem:
Here, the total number of people is \( n = 10 + 6 = 16 \) (10 men and 6 women), and we need to choose \( r = 5 \) people.

\[
\text{Number of ways} = \binom{16}{5} = \frac{16!}{5!(16-5)!} = \frac{16!}{5! \times 11!}
\]

Now, let's calculate it:

\[
\binom{16}{5} = \frac{16 \times 15 \times 14 \times 13 \times 12}{5 \times 4 \times 3 \times 2 \times 1} = \frac{524160}{120} = 4368
\]

### Conclusion:
There are **4,368 ways** to select a committee of 5 people from a group of 10 men and 6 women when there are no restrictions.

Would you like more details or have any questions?

Here are 5 related questions for further exploration:
1. How many ways can a committee of 3 men and 2 women be selected from this group?
2. How many ways can a committee be formed if it must include at least 1 woman?
3. How many ways can a committee of 4 people be selected from the group?
4. What if the committee must consist of exactly 2 men and 3 women? How many ways can this be done?
5. How many ways can a committee be formed if one particular man must be included?

**Tip:** Understanding the combination formula is essential when dealing with selection problems where order does not matter.

Explore how to determine the number of ways to select a committee of 5 people from a group of 10 men and 6 women using the combination formula. Learn step-by-step with detailed calculations and understand the basics of combinations in combinatorics.

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