Exam

JEE Main

Year

2019

Date

8 April

Shift

Morning Shift

Subject

Mathematics

Chapter

Permutation and Combination

JEE Main 2019 · 8 April · Morning Shift · Mathematics · Permutation and Combination

All possible numbers are formed using the digits 1, 1, 2, 2, 2, 2,...

All possible numbers are formed using the digits $1, 1, 2, 2, 2, 2, 3, 4, 4$ taken all at a time. The number of such numbers in which the odd digits occupy even places is

Step-by-step solution

Odd digits: $1, 1, 3$
Even digits: $2, 2, 2, 2, 4, 4$
The number of ways of placing odd digits at even position $= C3 4 \times \dfrac{3 !}{2 !} = 4 \times 3 = 12$
The number of ways of placing even digits $= \dfrac{6 !}{4 ! 2 !} = 15$
$∴$ Total number of ways $= 12 \times 15 = 180$