Question

Lennox must make two dentist appointments in November. He writes the numbers from 1 to 30 on papers to represent the days that he could go to the dentist, puts them in a bag, and pulls two papers at random from the bag without replacement. What is the probability that both appointments will be within the first five days of November?​

Answer 1

Answer: $\dfrac{2}{87}$

Step-by-step explanation:

Given

Lennox marks 30 papers to represent the dates

He has to choose two papers marked 1 to 5 to get the appointment within the first five days of November

This can be done in $^5C_2$ ways

The total no of ways is $^{30}C_2$

Probability is

$\Rightarrow P=\dfrac{^5C_2}{^{30}C_2}=\dfrac{5\times 4}{30\times 29}\\\\\Rightarrow P=\dfrac{2}{87}$