Q. 25

# How many 3 - digit numbers are there, with distinct digits, with each digit odd?

Answer :

In the question, it is given that we have to find three - digit numbers with distinct digits which means the digits should be nonrepeating and all the digits should be odd means no even digit.

Numbers by which we form the three digit numbers are 1, 3, 5, 7, 9 only the odd ones.

We will use the concept of multiplication because we have three sub jobs and each job is dependent on the other because a number selected on hundred’s place will not appear in ones and tens place.

The number of ways in which we can form three - digit numbers with odd digits is , 5 × 4 × 3 = 60.

We can also do it by 3 × 4 × 5 = 60 , there are total of 5 choices in the first digit on any place then it becomes 4 in the second digit place because some number has been placed in the first digit out of 5 , so out of rest 4 numbers one number is again consumed at second place so at the end 3 numbers are left to fit the last and third place of our 3 digit number.

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