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JEE Main 202529 JanuaryMorning Shift
Exam
JEE Main
Year
2025
Date
29 January
Shift
Morning Shift
Subject
Mathematics
Chapter
Permutation and Combination

JEE Main 2025 · 29 January · Morning Shift · Mathematics · Permutation and Combination

Let P be the set of seven digit numbers with sum of their digits...

Let P be the set of seven digit numbers with sum of their digits equal to 11 . If the numbers in P are formed by using the digits 1,2 and 3 only, then the number of elements in the set PP is :

Options

  1. A173
  2. B164
  3. C158
  4. D161

Correct answer

D. 161

Step-by-step solution

(i) number of numbers created using 1111133=7!5!2!⇒211111133=\frac{7!}{5!2!} \Rightarrow 21 (ii) number of numbers created using 1111223=7!4!2!⇒1051111223=\frac{7!}{4!2!} \Rightarrow 105 (iii) number of numbers created using 1112222=7!4!3!⇒351112222=\frac{7!}{4!3!} \Rightarrow 35 Total =161=161
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