Question

A letter lock consists of three rings each marked with $ 5 $ different letters. Number of maximum attempts to open the lock is:
A. $ 124 $
B. $ 125 $
C. $ 120 $
D. $ 75 $

Answer 1

Hint: Find the number of ways of choosing the letter for each of the three rings and then multiply the number of ways to open all the locks of the letter lock. We can also use concepts of permutations and combinations to solve such problems.

Complete step-by-step answer:
A letter lock consists of three rings each marked with $ 5 $ different letters.
As per given that the letter lock consists of three rings each marked with $ 5 $ different letters.
So, the number of ways for opening the first ring is equal to $ 5 $ as it is marked with $ 5 $ different letters.
In a similar manner, the number of ways for opening the second ring is equal to $ 5 $ as it is marked with $ 5 $ different letters.
In a similar manner, the number of ways for opening the third ring is equal to $ 5 $ as it is marked with $ 5 $ different letters.
So, the total number of ways of opening the letter lock will be the product of all the number of ways for opening the rings.
So, the number of ways for opening the letter lock is equal to $ 5 \times 5 \times 5 = 125 $ .
So, the number of maximum attempts to open the lock is equal to $ 125 $
So, the correct answer is “Option B”.

Note: Use the multiplication rule to find the number of attempts to unlock the letter lock by checking the number of ways to open each ring of the lock and then multiply the number of ways for each ring.