Question

The number of $3$ digit numbers lying between $100$ and $999$ inclusive and having only two consecutive digits identical is

• A. $100$
• B. $162$
• C. $150$
• D. $130$

Answer 1

The correct option is B $162$

Since we need only two consecutive digit identical so

Case.1 : first digit different and 2,3 are same means yxx.

so y has digit has 9 options to fill because 0 is excluded and x has also 9 option to fill because of digit other than y.

so in this case there are 81 ways.

Case 2 : 1,2 identical and 3 different i.e, bba

since b is first digit so it can't be 0 so b has 9 ways to fill and a has also 9 option left to fill because of b.

so, also in this case there are 81 ways.

so, no. of digits are 81+81=162

$\therefore$ so, the answer is B.162.