#### Directions : Question are Assertion- Reason type questions. Each of these questions contains two statements. Statement-1 (Assertion) and Statement-2 (Reason). Each of these questions also has four alternative choices,only one of which is the correct answer. You have to select the correct choice:Question: Four numbers are chosen at random (without replacement) from the set {1, 2, 3, ..., 20}.Statement-1 : The probability that the chosen numbers when arranged in some order will form an A.P. is   .Statement-2 : If the four chosen numbers form an A.P., then the set of all possible values of common difference is {±1, ±2, ±3, ±4, ±5}. Option 1) Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1. Option 2) Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1. Option 3) Statement -1 is true, statement -2 is false. Option 4) Statement -1 is false, statement -2 is true.

As we learnt in

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as

- wherein

Where n repeated experiment and E occurs r times.

If 4 numbers are chosen for an AP.

Out of {1, 2,3,  ----------- , 20}

Common differences can be

It cann't be

Total outcomes

Favourable sets  (with all differences)

Probability

Option 1)

Statement -1 is true, statement -2 is true ; statement -2 is a correct explanation of statement-1.

Incorrect

Option 2)

Statement -1 is true, statement -2 is true ; statement -2 is not a correct explanation of statement-1.

Incorrect

Option 3)

Statement -1 is true, statement -2 is false.

Correct

Option 4)

Statement -1 is false, statement -2 is true.

Incorrect