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JEE Main 202624 JanuaryMorning Shift
Exam
JEE Main
Year
2026
Date
24 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2026 · 24 January · Morning Shift · Mathematics · Permutation and Combination

The number of numbers greater than 5000, less than 9000 and...

The number of numbers greater than 5000, less than 9000 and divisible by 3, that can be formed using the digits 0,1,2,5,90,1,2,5,9, if the repetition of the digits is allowed, is ____\_\_\_\_

Correct answer

42

Step-by-step solution

(1) all different
5,0,1,9⇒⌊3=65, 0, 1, 9 \Rightarrow \lfloor 3 = 6 ways
(2) 2 alike, 2 different
5,0,0,1⇒35, 0, 0, 1 \Rightarrow 3 ways
5,1,1,2⇒35, 1, 1, 2 \Rightarrow 3 ways
5,2,2,0⇒35, 2, 2, 0 \Rightarrow 3 ways
5,2,2,9⇒35, 2, 2, 9 \Rightarrow 3 ways
5,5,0,2⇒65, 5, 0, 2 \Rightarrow 6 ways
5,5,2,9⇒65, 5, 2, 9 \Rightarrow 6 ways
5,1,9,9⇒35, 1, 9, 9 \Rightarrow 3 ways
(3) 3 alike, 1 different
5,5,5,0⇒35, 5, 5, 0 \Rightarrow 3 ways
5,5,5,9⇒35, 5, 5, 9 \Rightarrow 3 ways
(4) 2 alike, 2 other alike
5,5,1,1⇒35, 5, 1, 1 \Rightarrow 3 ways
Total ways =42= 42
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