an executive committee of three is selected from a group of ten which expression best describes the number of combinations.
What are your choices?
10P3 10! 3C10 10P3/31
To determine the number of combinations for selecting an executive committee of three from a group of ten, we can use the concept of combination.
The formula for combination is given by:
C(n, r) = n! / (r!(n-r)!)
Where:
- n is the total number of items or elements in the group
- r is the number of items to be selected
In this case, we want to select a committee of three from a group of ten, so n = 10 and r = 3.
Plugging these values into the formula, we get:
C(10, 3) = 10! / (3!(10-3)!)
Simplifying further, we have:
C(10, 3) = 10! / (3! * 7!)
Now, let's calculate the values of the factorials involved:
10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
3! = 3 * 2 * 1
7!
= 7 * 6 * 5 * 4 * 3 * 2 * 1
Now we can substitute these values into the formula:
C(10, 3) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((3 * 2 * 1) * (7 * 6 * 5 * 4 * 3 * 2 * 1))
After simplification, we get:
C(10, 3) = 10 * 9 * 8 / (3 * 2 * 1)
Calculating the values:
C(10, 3) = 720 / 6
Finally, the result is:
C(10, 3) = 120
Therefore, the number of combinations for selecting an executive committee of three from a group of ten is 120.