Question

4 integers are chosen from 9 to 20 what the probability that two of them are divisible by 5

Answer 1

It isn't mentioned whether  exactly two or two or more shall be considered. I'm assuming exactly two. Note that in such questions, it is normally assumed so.

Answer: 12/110.

[9, 20]

The numbers divisible by 5 in this range are 10, 15 and 20.

We'll first include any two out of these, by selecting: $^3C_{2}$ = 3.

Next, we'll have to select 2 more, which are not divisible by 5, to satisfy the criteria that exactly 2 out of the 4 we select are.

These shall be selected from a subset of 9 numbers.

Hence, number of ways of selecting = $^9C_{2}$ = 36.

The total possibilities are hence: 3 * 36 = 108.

Now, the total number of ways of selecting 4 numbers from the given range, are: $^1^2C_{4}$ = 495.

The probability is hence 108/495 = 12/110.