Solution -

We can use the combination concept here without using the formula.
Combinations are easy-going and the order doesn’t matter.

In Quantity A, they are asking for Probability.
Probability of an Event (P) = Number of Desired Outcome / Total Number of Possible Outcome

First we will consider the Number of Desired Outcome-

So, we are selecting both A and B i.e., two people. Out of 40 people, we are picking A and B.
We have 40 choices for the first person (say A), and, for the second person (i.e., B) we have 39 choices.
We are choosing two people but we are not mentioning the order. Thus, any way you choose them, it doesn't make any difference.

Now, what should we do to get rid of repetitions? - To get rid of the repetition of similar combinations; we'll divide the result by a factorial of 2.

Why 2!? - Because the number of elements in the numerator is two, as shown below:

So, the first part will be - (40*39)/2!

Now, looking into the next part i.e., where we will consider the Total Number of Possible Outcome-

Here, also we are selecting both A and B i.e., two people, but here, out of 100 people, we are picking A and B.
We have 100 choices for the first person (say A), and, for the second person (i.e., B) we have 99 choices.

We will use the same logic, and thus, the second part will be - (100*99)/2!

Finally we use the probability formula, i.e., Probability of an Event (P) = Number of Desired Outcome / Total Number of Possible Outcome

=> [(40*39)/2!] / [(100*99)/2!]

By reducing the above fraction, we get 26/165

Thus, Quantity A is 26/ 165

Quantity B is also 26 / 165

Thus, Quantity A = Quantity B

The Correct Answer Choice is C

KarunMendiratta used the Reverse Probability Method.
SeaOyster1 used the Slot Method.

Nice to see both methods side by side.

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