Question Detail
Question
In how many ways 7 pictures can be hanged on 9 pegs?
Correct Answer
Option B is the correct answer.
Detailed Explanation
We have 7 distinct pictures and 9 distinct pegs. Since the pictures are distinct and the pegs are distinct, the order in which the pictures are hung on the pegs matters.This is a permutation problem where we choose 7 pegs out of 9 and arrange the 7 pictures on them.The number of ways = 9P7.9P7 = 9! / (9-7)! = 9! / 2! = (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1) / (2 × 1) = 181,440.
Hint
Since both the items (pictures) and the positions (pegs) are distinct, and the arrangement matters, it's a permutation problem.