IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 23 : The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is

1. 5250
2. 6240
3. 2520
4. 3360

Video Explanation

Explanatory Answer

In the 5-digit number, the odd places should have odd digits, but the even places can have either even or odd. The only condition is that the digits should be distinct, which means that any digit cannot occur more than once in the number.

So out the 5 odd digits 1, 3, 5, 7, 9 we can choose one to fill in the first place in 5 different ways, after this we can choose an odd number to fill in the third place in 4 different ways and finally we can choose the odd number for the last place 3 different ways


In the remaining two places we can place the remaining any two of the remaining 7 numbers such that

So the number of ways a 5-digit number can be made such that the odd places get filled by odd numbers and distinct digits is
(5 * 4 * 3) * (7 * 6) = 60 * 42
= 2520

The question is " The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is "

Hence, the answer is '2520'

Choice C is the correct answer.