Question

You need to arrange ten of your favorite photographs on a mantle above a fireplace. How many ways can you arrange the photographs, assuming that the order of the pictures makes a difference to you.

Answer 1

The number of ways to arrange ten photographs on a mantle is calculated using permutations, specifically 10 factorial, which results in 3,628,800 different arrangements.

Step-by-step explanation:

The question asks how many different ways you can arrange ten photographs. This is a problem of permutations, where the order is important. To calculate the number of arrangements, or permutations, of ten photographs, we use the factorial of the number of items. Factorial is represented by an exclamation point (!) and means that you multiply the sequence of decrementing numbers from the number down to 1.

So, for ten photographs, the calculation is 10!, which is equal to:

10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 3,628,800.

Thus, there are 3,628,800 different ways to arrange the ten photographs on a mantle.