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 =   C 3 4 × 3 ! 2 ! = 4 × 3 = 12 The number of ways of placing even digits = 6 ! 4 !   2 ! = 15   ∴ Total number of ways = 12 × 15 = 180