To calculate P(6, 4), also known as the permutation of 6 items taken 4 at a time, we use the permutation formula:
P(n, r) = n! / (n – r)!
Where:
- n is the total number of items (in this case, 6),
- r is the number of items to choose (in this case, 4),
- ! denotes factorial, which is the product of all positive integers up to that number.
Using the values for this problem:
- n = 6
- r = 4
Now, calculate it step by step:
1. Calculate factorial of n: 6! = 6 × 5 × 4 × 3 × 2 × 1 = 720
2. Calculate factorial of (n – r): (6 – 4)! = 2! = 2 × 1 = 2
3. Now, substitute these values into the permutation formula:
P(6, 4) = 6! / (6 – 4)! = 720 / 2 = 360
Therefore, the result of P(6, 4) is 360.