Question

A three-digit number is written down at random. The probability that it will have two and only two consecutive identical place values is?

• A. $\frac{1}{45}$
• B. $\frac{3}{50}$
• C. $\frac{9}{50}$
• D. None

Answer 1

The correct option is A $\frac{1}{45}$

No. of $3$ digit numbers$=900$

No. of $3$ digit numbers with two consecutive identical place values$=C_1^{10}\times 2!$

Probability$=\frac{C_1^{10}\times 2!}{900}=\frac{10\times 2}{900}=\frac{1}{45}$