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Chapter 34: Problem 1080

In how many ways can we select a committee of 3 from a group of 10 people?

Short Answer

Expert verified
There are 120 ways to select a committee of 3 from a group of 10 people.

Step by step solution

01

Identify n and k

In our problem, there are 10 people in the group and we need to select a committee of 3. Therefore, n = 10 and k = 3.
02

Apply the combination formula

Now, we apply the combination formula to find the number of ways to select a committee of 3 from the group. Number of ways = C(10, 3) = \(\binom{10}{3}\) = \(\frac{10!}{3!(10-3)!}\)
03

Calculate factorials

Next, we will calculate the factorials in the formula: 10! = 10 脳 9 脳 8 脳 7 脳 6 脳 5 脳 4 脳 3 脳 2 脳 1 = 3,628,800 3! = 3 脳 2 脳 1 = 6 7! = 7 脳 6 脳 5 脳 4 脳 3 脳 2 脳 1 = 5,040
04

Substitute factorials into the formula and simplify

Now, substitute the factorials into the formula and simplify: Number of ways = \(\frac{10!}{3!(10-3)!}\) = \(\frac{3,628,800}{6 \times 5,040}\) Number of ways = \(\frac{3,628,800}{30,240}\) Number of ways = 120
05

Final answer

There are 120 ways to select a committee of 3 from a group of 10 people.

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