Question

Use the Permutation to determine the number of outcomes:
7p4

Answer 1

To calculate the number of permutations of 7 items taken 4 at a time (denoted as \(7P4\)), you can use the formula for permutations:

\[
nPr = \frac{n!}{(n-r)!}
\]

Where:
- \(n\) is the total number of items (in this case, 7)
- \(r\) is the number of items to choose (in this case, 4)
- \(n!\) represents the factorial of \(n\)

Plugging in the values:

\[
7P4 = \frac{7!}{(7-4)!} = \frac{7!}{3!}
\]

Calculating the factorials:

- \(7! = 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 = 5040\)
- \(3! = 3 \times 2 \times 1 = 6\)

Now, substituting the factorials into the permutation formula:

\[
7P4 = \frac{5040}{6} = 840
\]

Thus, the number of outcomes for \(7P4\) is **840**.