JEE Main 2020MathematicsPermutation CombinationMediumMCQ

JEE Main 2020 — Permutation Combination Question with Solution

JEE Main 2020 (07 Jan Shift 1)

Question

Total number of 6- digit numbers in which only and all the five digits 1,3,5,7 and 9 appears, is

Choose an option

Show full solutionCorrect option: D
Correct answer
D526!

Step-by-step explanation

As we have to make a six-digit number by using all the digits 1, 3, 5, 7, 9, hence exactly one of the digits is repeating.

For the digit to repeat we have 5C1=5 choices.
And, six digits in which one is repeating can be arranged in 6!2! ways.
Hence, total such numbers =5×6!2!=526!.

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About this question

This is a previous-year question from JEE Main 2020, covering the Permutation Combination chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.