There are 30 students auditioning for new openings in a chorus. How many ways can you choose 4 students to be in the chorus?
30*29*28*27=657720
Correct
Cool!!! Wasn't sure on that one
I believe that would be the number of ways they could be arranged. If you don't care about the order, then it would be
30*29*28*27/4! = 27405
Thank you Steve!!!!
To determine the number of ways to choose 4 students out of 30 for the chorus, we can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r! * (n - r)!)
Where nCr represents the number of ways to choose r items out of a set of n items, and ! denotes the factorial of a number.
In this case, we have n = 30 (total number of students) and r = 4 (number of students to be chosen for the chorus).
Using the formula, we can calculate the number of ways as follows:
30C4 = 30! / (4! * (30 - 4)!)
Simplifying this expression gives us:
30C4 = 30! / (4! * 26!)
Now let's break down the components of this expression:
- 30! represents the factorial of 30, which means multiplying all positive integers from 1 to 30 together.
- 4! represents the factorial of 4, which means multiplying all positive integers from 1 to 4 together.
- 26! represents the factorial of 26, which means multiplying all positive integers from 1 to 26 together.
Calculating these factorials:
30! = 30 * 29 * 28 * ... * 2 * 1
4! = 4 * 3 * 2 * 1
26! = 26 * 25 * 24 * ... * 2 * 1
Canceling out common terms from the numerator and denominator leaves us with:
30C4 = (30 * 29 * 28 * 27 * 26 * 25 * 24 * ... * 2 * 1) / (4 * 3 * 2 * 1 * 26 * 25 * 24 * ... * 2 * 1)
Simplifying further:
30C4 = (30 * 29 * 28 * 27) / (4 * 3 * 2 * 1)
Calculating this expression:
30C4 = 27,720
Therefore, there are 27,720 ways to choose 4 students to be in the chorus from a pool of 30 students.