Question

The number of numbers that can be formed by the digits 1, 2, 3, 4, 3, 2, 1 with the odd digits at odd places is

• A. 430
  
• B. 36
  
• C. 18
  
• D. None of these

Answer 1

The correct option is C

18

There are 4 odd places and there are 4 odd numbers viz 1,1,3,3. These four numbers can be arranged in four places in $\frac{4!}{2!2!}=6$ ways.
In a seven digit number there are 3 even places namely 2nd, 4th and 6th in which 3 even numbers 2, 2, 4 can be arranged in $\frac{3!}{2!}=3$ ways
Hence, the total number of numbers =$6\times 3=18$