Question

Use the combination formula to solve a problem when

n=6 and r=4.
a. 60
b. 45
c. 30
d. 15

Answer 1

Using the combination formula with n=6 and r=4, the result is 15, which is calculated using C(n, r) = n! / [r! (n-r)!]. None of the given options (60, 45, 30, 15) match the calculated result.

Step-by-step explanation:

To solve the problem using the combination formula with n=6 and r=4, we utilize the formula for combinations, which is C(n, r) = n! / [r! (n-r)!]. Here, n represents the total number of items, and r represents the number of items to choose. Let's calculate the combination:

1. Compute factorial for n (n!) which is 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720.
2. Calculate factorial for r (r!) which is 4! = 4 x 3 x 2 x 1 = 24.
3. Subtract r from n and compute factorial for (n-r), which is (6-4)! = 2! = 2 x 1 = 2.
4. Insert these values into the formula: C(6, 4) = 720 / (24 x 2) = 720 / 48 = 15.

Thus, when n=6 and r=4, using the combination formula, the result is 15. Therefore, the correct answer is not listed among the given options, and it seems like there may have been a mistake in the options provided or in the interpretation of the question.