Question

Evaluate the given expression and express the result using the usual format for writing numbers​ (instead of scientific​ notation). 45 Upper P 2

Answer 1

Answer:

$45P2 = 45*44=1980$

Step-by-step explanation:

Previous concepts

A permutation, "also called an arrangement number, is a rearrangement of the elements of an ordered list S into a one-to-one correspondence with S itself. The number of permutations on a set of n elements is given by n! factorial".

The formula for permutation is given by:

$nPx =\frac{n!}{(n-x)!}$

Solution to the problem

We are interested in find 45P2, if we use the last formula we got this:

$45P2 = \frac{45!}{(45-2)!}=\frac{45!}{43!}$

Now we can use the following property for the factorial operation:

$n! = n (n-1)!$

So using this two times we can rewrite the expression 45! on this way:

$45! = 45* 44!$

$45! = 45*44* 43!$

And replacing this we got:

$45P2 = \frac{45!}{(45-2)!}=\frac{45*44*43!}{43!}$

We can cancel the 43! of the numerator with the 43! of the denominator and we got:

$45P2 = 45*44=1980$