The number of seven digits odd numbers, that can be formed using all the seven digits 1 ,   2 ,   2 ,   2 ,   3 ,   3 ,   5 is

Step-by-step solution

To find the number of 7 digit odd number formed by using the seven digits 1 , 2 , 2 , 2 , 3 , 3 , 5 We will take following cases, Case 1 - fixing 1 as unit place, So total number of ways will be 6 ! 3 ! 2 !   as  2   is repeating three times and 3 is repeating two times Case 2 - fixing 3 unit place, So total number of ways will be 6 ! 3 ! Case 3 - fixing 5 as unit place, So total number of ways will be 6 ! 3 ! 2 ! Now adding all the cases we will get, tota