Q. A five digit number is chosen at random. The probability that all the digit are distinct and digits at odd places are odd and digits at even place are even, is
A) $\frac{1}{60}$
B) $\frac{2}{75}$
C) $\frac{1}{50}$
D) $\frac{1}{75}$
Explanation
(d)
Total number of 5 digit number $= 9 \times 10 \times 10 \times 10 \times 10 = 90000$
Number of favourable numbers $= 5 \times 5 \times 4 \times 4 \times 3 = 12000$
Thus, required probability $= \frac{1200}{90000} = \frac{1}{75}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.