Question

The number of odd numbers lying between $40000$ and $70000$ that can be made from the digits $0,1,2,3,4,5,7$ if digits can be repeated in the same number is

• A. $864$
• B. $932$
• C. $766$
• D. None of these

Answer 1

The correct option is A $864$

The number of 5 digits having 4 or 5 in ten thousand's place and 1 or 5 in unit's place and the remaining digits with any of the given 6 digits is given by :

The number of ways to fill ten thousand's place$={{}^{2}P}_1=2$ and

The number of ways to fill unit's place$={{}^{2}P}_1=2$

Number of ways to fill other three places$=6^3$

So required number of numbers$={2\times 2\times 6}^3=864$