The number of seven digit odd numbers, that can be formed using all the seven digits 1, 2, 2, 2, 3, 3, 5 is _____.
Step-by-Step Solution
Key Concept: For odd numbers, units digit must be 1, 3, or 5. Fix units digit and count arrangements of remaining 6 digits.
If unit digit=5: remaining 1,2,2,2,3,3 $\to$ 6!/(3!2!)=60. If unit digit=3: remaining 1,2,2,2,3,5 $\to$ 6!/3!=120. If unit digit=1: remaining 2,2,2,3,3,5 $\to$ 6!/(3!2!)=60. Total=60+120+60=240.
Correct Answer: 240