Question

The number $2006$ is made up of exactly two zeros and two other digits whose sum is $8$. The number of $4$ digit numbers with these properties (including $2006$) is :

• A. $7$
• B. $18$
• C. $21$
• D. $24$

Answer 1

The correct option is D $24$

Two digit numbers whose sum can be $8$ are-

$17,26,35,44,53,62,71$

No. of numbers with $17,26,35=3(\frac{4!}{2!}-3!)=3(12-6)=18$

No. of numbers with $44=\frac{4!}{2!.2!}-\frac{3!}{2!}=6-3=3$

$\therefore$ Total no. of numbers with $17,26,35$ and $44=18+3=21$

Hence the correct answer is $21$.