Question

Six distinct numbers are selected from first $150$ natural numbers. The probability all the six numbers are divisible both by $3$ and $5$ is

• A. $1/33$
• B. $1/35$
• C. $1/49$
• D. none of these

Answer 1

The correct option is D none of these

Total number of ways of selecting 6 numbers out of 1, 2, ...., 150 is ${}^{150}{C}_6$.
A number is divisible by 3 and 5 both if and only if it is divisible by 15.
There are 10 numbers viz. 15, 30, ..., 150 that are divisible by 15.
Thus, probability of required event $=\frac{{}^{10}{C}_6}{{}^{150}{C}_6}$.