The value of `""^(10)P_(3)` is

Options

A. 504
B. 308
C. 720
D. 600

Answer

To find the value of \( {}^{10}P_{3} \), we can use the formula for permutations:

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

In this case, \( n = 10 \) and \( r = 3 \). Therefore, we can substitute these values into the formula:

\[ {}^{10}P_{3} = \frac{10!}{(10-3)!} = \frac{10!}{7!} \]

Next, we can express \( 10! \) in terms of \( 7! \):

\[ 10! = 10 \times 9 \times 8 \times 7! \]

Now, substituting this back into our equation gives:

\[ {}^{10}P_{3} = \frac{10 \times 9 \times 8 \times 7!}{7!} \]

The \( 7! \) in the numerator and denominator cancels out:

\[ {}^{10}P_{3} = 10 \times 9 \times 8 \]

Now, we can calculate \( 10 \times 9 \times 8 \):

1. First, calculate \( 10 \times 9 = 90 \).
2. Next, calculate \( 90 \times 8 = 720 \).

Thus, the value of \( {}^{10}P_{3} \) is:

\[ {}^{10}P_{3} = 720 \]

### Final Answer:
The value of \( {}^{10}P_{3} \) is \( 720 \).