Question

In how many ways can 4 singers be selected from 7 who came to an audition

Answer 1

To find the number of ways to select 4 singers from 7 who came to an audition, we can use the concept of combinations. The formula for combinations is C(n, r) = n! / (r!(n-r)!), where n is the total number of singers and r is the number of singers to be selected. Using this formula, we can calculate that there are 35 ways to select 4 singers from 7 who came to the audition.

Step-by-step explanation:

To find the number of ways to select 4 singers from 7 who came to an audition, we can use the concept of combinations. In this case, we want to select a group of 4 singers out of 7, without considering the order in which they are selected. The formula for combinations is given by C(n, r) = n! / (r!(n-r)!), where n is the total number of singers and r is the number of singers to be selected. Using this formula, we can calculate the number of combinations as follows:

1. Substitute n = 7 and r = 4 into the formula: C(7, 4) = 7! / (4!(7-4)!)
2. Calculate the factorials: C(7, 4) = 7! / (4!3!)
3. Expand the factorials: C(7, 4) = (7 * 6 * 5 * 4!) / (4! * 3 * 2 * 1)
4. Cancel out the common factorial terms: C(7, 4) = (7 * 6 * 5) / (3 * 2 * 1)
5. Simplify the expression: C(7, 4) = 35

Therefore, there are 35 ways to select 4 singers from 7 who came to the audition.

Answer 2

This math is known as permutations- the arrangement of a set of objects. A way that I use to solve these problems was by just multiplying the numbers, so the singer's can be selected in 28 ways.