A church has 8 bells in its bell tower. Before each church service 3 bells are rung in sequence. No bell is rungmore than once. How many sequences are there?
A) 336
B) 6720
C) 56
D) 13,440

Question

Quizplus · Accepted Answer

This problem can be solved using permutations since the order in which the bells are rung matters and no bell is rung more than once. The formula for permutations is nPr = n! / (n-r)!, where n is the total number of items to choose from, r is the number of items to choose, n! denotes the factorial of n, and (n-r)! is the factorial of the difference between n and r. Here, n = 8 (total bells) and r = 3 (bells to be rung in sequence). Thus, the number of sequences is 8P3 = 8! / (8-3)! = 8! / 5! = (8×7×6×5!) / 5! = 8×7×6 = 336.

A Church Has 8 Bells in Its Bell Tower