Question

Evaluate each of the following.
(a) P(8,4)
(b) C(8,4)

Answer 1

P(8,4) = 8! / (8-4)!
= 8*7*6*5
= 1680
C(8,4) = 8! / (4! (8-4)!
= 8*7*6*5/4*3*2*1
= 70

Answer 2

The calculated values of the expressions are

(a) P(8,4) = 1680

(b) C(8,4) = 70

How to determine the values of the expressions

From the question, we have the following parameters that can be used in our computation:

(a) P(8,4)

(b) C(8,4)

We can calculate P(8, 4) using the formula:

`P(n, k) = (n!)/((n-k)!)`

In this case, n = 8 and k = 4.

Plugging these values into the formula, we get:

`P(8, 4) = (8!)/((8-4)!) = (8 \cdot 7 \cdot 6 \cdot 5)/(4!) = 1680`

We can calculate C(8, 4) using the formula:

`C(n, k) = \binom{n}{k} = (n!)/(k!(n-k)!)`

So, we have

`C(8, 4) = \binom{8}{4} = (8!)/(4!4!) = (8 \cdot 7 \cdot 6 \cdot 5)/(4!4!) = 70`

Hence, the calculated values of the expressions are (a) P(8,4) = 1680 and (b) C(8,4) = 70