Question

Number of permutations of 5 distinct objects is:

• A. 25
• B. 60
• C. 120
• D. 720

Hint:

Permutations = Arrangements (Order matters). Combinations = Selections (Order doesn't matter). For 5 objects, there is only 1 way to select them all, but 120 ways to arrange them!

Answer 1

The Correct Option is C

To find the number of permutations of 5 distinct objects, we use the formula for permutations of \(n\) distinct objects, which is given by the factorial of \(n\), denoted by \(n!\).

In this scenario, the number of objects \(n = 5\). Therefore, the number of permutations is calculated as:

\(5! = 5 \times 4 \times 3 \times 2 \times 1\)

Now, we perform the multiplication step-by-step:

1. \(5 \times 4 = 20\)
2. \(20 \times 3 = 60\)
3. \(60 \times 2 = 120\)
4. \(120 \times 1 = 120\)

Therefore, the number of permutations of 5 distinct objects is 120.

Justification of the Answer:

• 25: This value does not align with the factorial calculation of 5 objects.
• 60: This value is incorrect; it represents an intermediate step in the calculation.
• 120: This is the correct number of permutations when properly multiplied.
• 720: This value represents the incorrect factorial of a higher number (6!), not 5.

Thus, the correct answer is 120.