Question

If \( n = 5 \) and \( r = 3 \), then the value of \( ^nP_r \) is:

• A. 20
• B. 30
• C. 50
• D. 60

Hint:

Use the formula \( ^nP_r = \frac{n!}{(n - r)!} \) for permutations to calculate the number of ways to arrange \( r \) objects out of \( n \) objects.

Answer 1

The Correct Option is B

Step 1: Understanding the permutation formula.
The formula for \( ^nP_r \) (permutation) is given by: \[ ^nP_r = \frac{n!}{(n - r)!} \]
Step 2: Applying the values.
Substituting \( n = 5 \) and \( r = 3 \) into the formula, we get: \[ ^5P_3 = \frac{5!}{(5 - 3)!} = \frac{5!}{2!} \] \[ 5! = 5 \times 4 \times 3 \times 2 \times 1 = 120 \quad \text{and} \quad 2! = 2 \times 1 = 2 \] \[ ^5P_3 = \frac{120}{2} = 60 \]
Step 3: Conclusion.
Thus, the value of \( ^5P_3 \) is 60. Final Answer:} 60.