Perform the indicated calculation.
$_{48}P_2 = \boxed{\quad}$ (Type a whole number.)
Answer (2)
To solve the problem of finding 48 P 2 , we need to understand what this permutation notation means.
The expression n P r represents the number of ways to arrange r items out of n items where order matters. The formula to calculate permutations is:
n P r = ( n − r )! n !
In the given problem, we have 48 P 2 , which means:
We have n = 48 items.
We want to arrange r = 2 of them.
Now, let's substitute the values into the formula:
48 P 2 = ( 48 − 2 )! 48 ! = 46 ! 48 !
The factorial notation n ! (read as "n factorial") means the product of all positive integers up to n . When we have a division like this with factorials, a lot of the terms will cancel out.
So, we can simplify:
48 P 2 = 46 ! 48 × 47 × 46 !
The 46 ! in the numerator and denominator cancels out, leaving us with:
48 P 2 = 48 × 47
Now, we just perform the multiplication:
48 × 47 = 2256
So, 48 P 2 = 2256 .
Therefore, the number of ways to arrange 2 items out of 48 is 2256.
The value of 48 P 2 is calculated as 2256 . This indicates that there are 2,256 ways to arrange 2 items from a total of 48 items. The calculation utilizes the permutation formula where order of selection matters.
;
