Question

The number of all three digit even number such that if $3$ is one of the digits, then next digit is $5$, is

• A. $359$
• B. $360$
• C. $365$
• D. $380$

Answer 1

The correct option is C $365$

We need even numbers so the last digit must be $0,2,4,6,8$. So $5$ possibilities

Now the ten's place can be any number between $0$ to $9$ except $3$ because in that case, the $3$ is to be followed by $5$ in the units place then it won't be an even no., so there are $9$ possibilities.

Now in hundred's place can be anything between $1$ to $9$ except $3$ because if $3$ is present then the next digit must be $5$ so there are $8$ possibilities.

Now if there is $3$ in hundred's place then $5$ will be in ten's place and the numbers must be $350,352,354,356,358$ which will be treated seperately. So $5$ possibilities

Therefore,

Total no. of even numbers $=8\times 9\times 5+5=365$