Question

How many ways can ten pictures be arranged three at a time?

1) 120
2) 210
3) 252
4) 720

Answer 1

The number of ways to arrange ten pictures three at a time is calculated using permutations without repetition; the answer is 720, which aligns with option 4.

Step-by-step explanation:

The student is asking about the number of ways to arrange ten pictures three at a time. This is a problem of permutations, where the order matters. To solve this, we use the formula for permutations without repetition, which is nPr = n! / (n - r)!, where n is the total number of items to choose from, and r is the number to arrange.

Here, we have 10 pictures and want to arrange 3 at a time, so we have:

10P3 = 10! / (10 - 3)! = 10! / 7! = (10 × 9 × 8) / (3 × 2 × 1) = 720.

Among the given options, 720 is the correct answer which corresponds to option 4.