Question

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 :

• A. 175
• B. 162
• C. 160
• D. 180

Answer 1

The Correct Option is D

The correct answer is D:180
Given that: The periodic number to be formed using digits \(1,1,2,2,2,2,2,3,4,4\) to be taken all at a time.
[Note: Means;it is a clear case of combination as only selection is important here]
\(\therefore 4_{C_{3}}\times\frac{3!}{2!}\times\frac{6!}{2!\times4!}=180\)  \((\therefore n_{c_{k}}=\frac{n!}{(n-k)!,k!})\)\((4_{c_{3}}=\frac{4!}{1!\times3!})\)