JEE Main 2021 — Probability Question with Solution
From: JEE Main 2021 (Online) 16th March Evening Shift
Question
Let A denote the event that a 6-digit integer formed by 0, 1, 2, 3, 4, 5, 6 without repetitions, be divisible by 3. Then probability of event A is equal to :
Choose an option
Show full solutionCorrect option: A
Correct answer
A
Step-by-step explanation
Total cases :
. . . . .
n(s) = 6 . 6!
Favourable cases :
Number divisible by 3 Sum of digits must be divisible by 3
Case - I
1, 2, 3, 4, 5, 6
Number of ways = 6!
Case - II
0, 1, 2, 4, 5, 6
Number of ways = 5 . 5!
Case - III
0, 1, 2, 3, 4, 5
Number of ways = 5 . 5!
n(favourable) = 6! + 2 . 5 . 5!
. . . . .
n(s) = 6 . 6!
Favourable cases :
Number divisible by 3 Sum of digits must be divisible by 3
Case - I
1, 2, 3, 4, 5, 6
Number of ways = 6!
Case - II
0, 1, 2, 4, 5, 6
Number of ways = 5 . 5!
Case - III
0, 1, 2, 3, 4, 5
Number of ways = 5 . 5!
n(favourable) = 6! + 2 . 5 . 5!
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This is a previous-year question from JEE Main 2021, covering the Probability 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.