The number of seven digits odd numbers, that can
be formed using all theseven digits 1, 2, 2, 2, 3, 3,
5 is \_\_\_\_\_\_\_\_\_\_\_\_.
Answer: 240
Solutions · 1
Official solution
For the number to be odd, the unit digit must be 5, 3, or 1 (odd digits present).
Unit digit 5: remaining digits 1,2,2,2,3,3 arranged in 6 places: 3!2!6!=60
Unit digit 3: remaining digits 1,2,2,2,3,5 arranged: 3!6!=120
Unit digit 1: remaining digits 2,2,2,3,3,5 arranged: 3!2!6!=60
\[\text{Total} = 60+120+60 = 240\]