Problem

Use the formula for ${ }_{n} P_{r}$ to evaluate the following expression. \[ { }_{6} \mathrm{P}_{3} \] \[ { }_{6} \mathrm{P}_{3}= \]

Solution

Step 1 :We are given the expression ${ }_{6} P_{3}$ and we are asked to evaluate it.

Step 2 :The formula for permutation is given by ${ }_{n} P_{r} = \frac{n!}{(n-r)!}$ where 'n' is the total number of items, 'r' is the number of items to choose, 'n!' is the factorial of 'n', and '(n-r)!' is the factorial of the difference between 'n' and 'r'.

Step 3 :In this case, 'n' is 6 and 'r' is 3. So, we need to calculate the factorial of 6, the factorial of (6-3), and then divide the two.

Step 4 :First, calculate the factorial of 6, which is 720.

Step 5 :Next, calculate the factorial of (6-3), which is 6.

Step 6 :Finally, divide the factorial of 6 by the factorial of (6-3) to get the permutation. The result is 120.

Step 7 :So, ${ }_{6} P_{3} = \boxed{120}$

From Solvely APP
Source: https://solvelyapp.com/problems/8295/

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