Question

Number of odd numbers of five distinct digits can be formed by the digits 0,1,2,3,4, is
(A) 24
(B) 120
(C) 48
(D) 36

Answer 1

Hint:For the arrangement of objects or numbers, the concept of permutation and combination is used.
In the given question, we have to find the number of odd digits that can be formed by the given numbers. Odd numbers are those numbers that don’t give whole numbers as the answer when divided by two, which means the number ends with 1,3,5…. Using this information, we can find out the correct answer.

Complete step by step answer:
The number required is odd so the last digit can be either 1 or 3.
So the number of options for the last digit of the 5 digit number is 2.

The first digit can’t be 0 and one of the odd numbers is already placed at the last digit so the number of options for the first digit of the 5 digit number is 3.

The second digit can be taken by 0 or any of the two numbers left that weren’t placed at the first or last digit, so the number of options for the second digit is 3.

2 numbers are left for taking the position at the third digit, so the number of options for the third digit is 2.

So, only 1 number can take place at the fourth digit.

Now, the number of 5 digits odd numbers that can be formed by the digits 0,1,2,3,4 = 3×3×2×1×2 = 36

Hence, option (D) is the correct answer.

Note:To arrange something in a group in a specific order, we use permutation but when we have to group something and the order of the elements doesn’t matter then we use the concept of combination.

In the given question, we are told to form odd 5 digit numbers specifically, thus the order of the numbers matter and that’s why we use permutation.