A school choir has 10 sopranos, 8 altos, 7 tenors and 5 basses. How many ways are there to select a barbershop quartet of two tenors and two basses?
Don't you just want
C(7,2)*C(5,2) ?
The fact that you have altos and sopranos has nothing to do with it.
To determine the number of ways to select a barbershop quartet of two tenors and two basses, we can follow these steps:
Step 1: Calculate the number of ways to select two tenors from the 7 available.
There are 7 tenors available, and we need to choose 2 of them. We can use the combination formula to calculate this:
C(7,2) = 7! / (2! * (7-2)!) = (7 * 6) / (2 * 1) = 21
So there are 21 ways to select two tenors from the 7 available.
Step 2: Calculate the number of ways to select two basses from the 5 available.
There are 5 basses available, and we need to choose 2 of them. Again, we can use the combination formula:
C(5,2) = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10
So there are 10 ways to select two basses from the 5 available.
Step 3: Multiply the results from steps 1 and 2 together.
To find the total number of ways to select a barbershop quartet of two tenors and two basses, we multiply the results from steps 1 and 2:
21 * 10 = 210
Therefore, there are 210 ways to select a barbershop quartet of two tenors and two basses from the given school choir.
To find the number of ways to select a barbershop quartet of two tenors and two basses, we can use the concept of combinations.
First, let's find the number of ways to select two tenors out of 7. This can be calculated using the combination formula "nCr" which represents choosing "r" items from a set of "n" items without regard to their order. In this case, we have 7 tenors to choose from and we want to select 2, so the calculation is:
C(7, 2) = 7! / (2! * (7-2)!) = (7 * 6) / (2 * 1) = 21
Next, let's find the number of ways to select two basses out of 5. Using the same combination formula:
C(5, 2) = 5! / (2! * (5-2)!) = (5 * 4) / (2 * 1) = 10
Finally, we can find the total number of ways to select a barbershop quartet by multiplying the number of ways to choose tenors and basses:
Total number of ways = C(7, 2) * C(5, 2) = 21 * 10 = 210
Therefore, there are 210 ways to select a barbershop quartet consisting of two tenors and two basses from the given choir.