Question

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

Answer 1

Correct Answer: 240

Digits are 1,2,2,2,3,3,5 
If unit digit 5 , then total numbers \(=\frac{6!}{3!2!}=60\)
If unit digit 3 , then total numbers \(=\frac{6!}{3!} =120\)
If unit digit 1 , then total numbers \(=\frac{6!}{3!2!}=60\)
∴ total numbers =60+60+120=240
So , the correct answer is 240

Answer 2

Digits are \( 1, 2, 2, 2, 3, 3, 5 \). If unit digit is 5, then total numbers are: \[ \frac{6!}{3!2!} = 60 \] If unit digit is 3, then total numbers are: \[ \frac{6!}{3!} = 120 \] If unit digit is 1, then total numbers are: \[ \frac{6!}{3!2!} = 60 \] Therefore, total numbers are: \[ 60 + 60 + 120 = 240 \]