Question

Dialing a telephone number an old man forgets the last two digits remembering only that these are different dialed at random. The probability that the number is dialed correctly is

• A. $\frac{1}{45}$
• B. $\frac{1}{90}$
• C. $\frac{1}{100}$
• D. none of these

Answer 1

The correct option is B

$\frac{1}{90}$

Explanation for the correct answer:

We know that, Total number of digits is $\left\{0,1,2,3,4,5,6,7,8,9\right\}=10$

number of ways dialing last two digits is ${}^{10}C_2\times 2!=\frac{10!}{8!2!}\times 2!=90$

number of way to Correct number is $1$

The probability that the number is dialed correctly is $\frac{1}{90}$

Hence, correct answer is option $\left(B\right)$