Question

Evaluate the expression P(12,9)=_____

Answer 1

Answer:

The value of P(12,9) is 79833600.

Step-by-step explanation:

We need to find the value of P(12,9).

The given expression represents the permutation.

The formula for permutation is

$P(n,r)=\frac{n!}{(n-r)!}$

In the given expression n=12 and r=9. So, the value of P(12,9) is

$P(n,r)=\frac{12!}{(12-9)!}$

$P(n,r)=\frac{12!}{3!}$

$P(n,r)=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3!}{3!}$

Now, cancel out the common factors.

$P(n,r)=12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4$

$P(n,r)=79833600$

Therefore the value of P(12,9) is 79833600.

Answer 2

$P(12,9)=\dfrac{12!}{3!}=4\cdot5\cdot\ldots\cdot11\cdot12=79,833,600$