Question

Use the permutation formula below to find the number of outcomes when n = 10 and r = 6.

n!/ (n-r)!
a) 10
b) 720
c) 5040
d) 360

Answer 1

The number of outcomes for n = 10 and r = 6 using the permutation formula is 151,200.

Step-by-step explanation:

To find the number of outcomes using the permutation formula when n = 10 and r = 6, we calculate 10! (ten factorial) divided by (10-6)! (four factorial). The factorial of a number, such as 10!, is the product of all positive integers up to that number (i.e., 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1).

Let's perform the calculation step by step:

1. 
   
3. Compute 10!: 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.
4. 
   
6. Compute 4! (since 10-6=4): 4 x 3 x 2 x 1 = 24.
7. 
   
9. Divide 10! by 4!: 3,628,800 / 24 = 151,200.

Therefore, the number of outcomes for n = 10 and r = 6 is 151,200, which is not one of the provided options.