Q. 30

A number lock on a suitcase has 3 wheels each labeled with ten digits 0 to 9. If the opening of the lock is a particular sequence of three digits with no repeats, how many such sequences will be possible? Also, find the number of unsuccessful attempts to open the lock.

Answer :

In the question, we have to find the possible number of 3 digit numbers formed by the numbers 0 to 9 when repetition of digits is not allowed.

We will use the concept of multiplication because there are three sub jobs dependent on each other because a number appearing on any one place will not appear in any other place.


In the first position from left we will have ten choices, in the second position we will have nine choices, and in the third position, we will have eight choices because repetition is not allowed and one digit is occupied in each position.


The number of ways in which we can form three - digit numbers with the help of given data is 10 × 9 × 8 = 720


There will be only one correct combination out of these so the incorrect combinations will be 720 - 1 = 719


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