Question

Help. Find the value of each expression.

9P3

10C4

Answer 1

nPr = n! / (n - r)! 

number of permutations of 9, taken 3 at a time

9P3 = 9! / (9 -3)!
9P3 = 9! / 6!
9P3 = 9 x 8 x 7 
9P3 = 504 

nCr = n! / r! (n - r)! 

the number of combinations of 10, taken 4 at a time.

10C4 = 10! / 4! (10 - 4)! 
10C4 = 10! / 4! 6! 
10C4 =10 x 9 x 8 x 7 / 4 x 3 x 2 x 1
10C4 = 5040 / 24
10C4 = 210

Answer 2

The number of permutations of 9, taken 3 at a time is 504 and the number of combinations of 10, taken 4 at a time is 204.

Here we have to determine the permutation and combination

9P3

10C4

P-Permutation(arrangement)

C-Combination(selection)

What is the formula for the permutation?

$nPr = n! / (n - r)!$

The number of permutations of 9, taken 3 at a time

$9P3 = 9! / (9 -3)!\\9P3 = 9! / 6!\\9P3 = 9 \times 8 \times 7 \\9P3 = 504$

What is the formula for the combination?

$nCr = n! / r! (n - r)!$

The number of combinations of 10, taken 4 at a time.

$10C4 = 10! / 4! (10 - 4)! \\10C4 = 10! / 4! 6! \\10C4 =10 \times 9 \times 8 \times 7 / 4 \times 3 \times 2 \times 1\\10C4 = 5040 / 24\\10C4 = 210$

To learn more about the permutation and combination visit:

https://brainly.com/question/11732255