Question Detail
Question
In how many ways can 7 pictures be hanged on 9 pegs?
Correct Answer
Option A is the correct answer.
Detailed Explanation
This is a permutation problem because the order in which the pictures are hung on the pegs matters (e.g., Picture 1 on Peg A and Picture 2 on Peg B is different from Picture 2 on Peg A and Picture 1 on Peg B). We need to arrange 7 distinct pictures out of 9 distinct pegs. The formula for permutations is P(n, r) = n! / (n-r)!. Here, n=9 (pegs) and r=7 (pictures). So, the number of ways is P(9, 7) = 9! / (9-7)! = 9! / 2! = 181,440.
Hint
Since each picture is distinct and each peg is distinct, and the placement of pictures matters, this is a permutation problem.