In how many ways can a committee of 4 people be chosen out of 8 people?

<h2>Question</h2>

In how many ways can a committee of 4 people be chosen out of 8 people?

<h2>Choices</h2>

• 32

• 70

• 110

• 126

<h2>Correct Answer: 70</h2><h2>Explanation</h2>

To solve this problem, we use the concept of combinations. Combinations are a way to select items from a larger pool, where the order of selection does not matter.

The formula to calculate combinations is given by:

$$ C(n, k) = \frac{n!}{k!(n-k)!} $$

where:

• n is the total number of items

• k is the number of items to choose

• n! denotes the factorial of n, which is the product of all positive integers up to n.

In this case, we have 8 people and we want to choose a committee of 4. So, n = 8 and k = 4.

Substituting these values into the combination formula, we get:

$$ C(8, 4) = \frac{8!}{4!(8-4)!} $$

$$ = \frac{8!}{4! \cdot 4!} $$

$$ = \frac{8 \times 7 \times 6 \times 5 \times 4!}{4! \times 4 \times 3 \times 2 \times 1} $$

$$ = \frac{8 \times 7 \times 6 \times 5}{4 \times 3 \times 2 \times 1} $$

$$ = \frac{1680}{24} $$

$$ = 70 $$

<h2>Conclusion</h2>

Thus, the number of ways to choose a committee of 4 people from a group of 8 people is 70. This makes the correct answer 70.