Problem

Evaluate the expression. \[ { }_{10} \mathrm{P}_{3} \] A. 720 B. 27 C. 120 D. 7

Solution

Step 1 :The given expression is a permutation, which is a way of arranging items where the order is important. In this case, we are asked to find the number of ways to arrange 3 items out of 10.

Step 2 :The formula for permutations is: \(nPr = \frac{n!}{(n-r)!}\) where n is the total number of items, r is the number of items to choose, and ! denotes factorial, which is the product of all positive integers up to that number.

Step 3 :So, we need to calculate 10P3 using this formula.

Step 4 :Let n = 10 and r = 3.

Step 5 :Substitute the values into the formula, we get \(10P3 = \frac{10!}{(10-3)!}\).

Step 6 :Evaluating the expression, we get the result as 720.

Step 7 :Final Answer: \(\boxed{720}\)

From Solvely APP
Source: https://solvelyapp.com/problems/20749/

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