find the value of the permutation
12P0
anythingP0 = 1
There is only 1 way to choose nothing.
To find the value of the permutation 12P0, we need to understand what a permutation is and how it is calculated.
In mathematics, a permutation of a set is an arrangement of its elements in a specific order. The number of permutations can be calculated using the formula:
P(n, r) = n! / (n - r)!
where "n" is the total number of items in the set and "r" is the number of items taken at a time.
In the case of 12P0, we have a total of 12 items (n) and we are taking 0 items at a time (r).
Using the formula, we substitute these values:
P(12, 0) = 12! / (12 - 0)!
Since r is 0, the denominator becomes 12 - 0 = 12, and any number factorial divided by 1 is equal to the number itself.
Therefore, 12! / (12 - 0)! becomes 12! / 12!.
Now, calculating 12!, which means multiplying all the numbers from 12 down to 1:
12! = 12 x 11 x 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1
= 479,001,600
Also, calculating (12 - 0)!, which means multiplying all the numbers from 12 down to 1 again:
(12 - 0)! = 12! = 479,001,600
Now, we can substitute these values back into the permutation formula:
12P0 = 12! / (12 - 0)!
= 479,001,600 / 479,001,600
= 1
Therefore, the value of the permutation 12P0 is 1.