The image contains handwritten text: "7w Sm" and "4 member commit". It seems the problem wants us to figure out how many small committees can be formed if you have a total of 7 people and each committee consists of 4 members. This is a combination problem.

1. Problem Description

The image contains handwritten text: "7w Sm" and "4 member commit". It seems the problem wants us to figure out how many small committees can be formed if you have a total of 7 people and each committee consists of 4 members. This is a combination problem.

2. Solution Steps

We need to calculate the number of ways to choose 4 members from a group of

7. This is a combination problem, because the order in which the members are chosen does not matter. The formula for combinations is:

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

where $n$ is the total number of items (in this case, 7 people), and $k$ is the number of items to choose (in this case, 4 members).

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

Plugging in the values $n = 7$ and $k = 4$ into the formula, we get:

$C(7, 4) = \frac{7!}{4!(7-4)!}$

$C(7, 4) = \frac{7!}{4!3!}$

$C(7, 4) = \frac{7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(4 \times 3 \times 2 \times 1)(3 \times 2 \times 1)}$

$C(7, 4) = \frac{7 \times 6 \times 5}{3 \times 2 \times 1}$

$C(7, 4) = \frac{7 \times 6 \times 5}{6}$

$C(7, 4) = 7 \times 5$

$C(7, 4) = 35$

3. Final Answer

There are 35 possible 4-member committees that can be formed from a group of 7 people.