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