Question

An art gallery plans to display 7 sculptures in a single row. How many different arrangements of the sculptures are possible?

A. (7)
B. (42)
C. (5040)
D. (49)

Answer 1

The number of different arrangements of the 7 sculptures is 5040.

Step-by-step explanation:

To calculate the number of different arrangements of the sculptures in a single row, we can use the concept of permutation. A permutation is an arrangement of objects in a specific order. To find the number of permutations of 7 sculptures, we can use the formula for permutations: P(n,r) = n! / (n-r)!, where n is the total number of objects and r is the number of objects we are arranging.

1. Plug in the values: n = 7 and r = 7 (since we are arranging all 7 sculptures).
2. Calculate n! (7 factorial) = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040.
3. Calculate (n-r)! (0 factorial) = 1.
4. Divide n! by (n-r)! = 5040 / 1 = 5040.

Therefore, the number of different arrangements of the 7 sculptures is 5040. Thus, the correct answer is C. (5040).