Question

An online programming test has a question bank of 8 different questions and each student is asked 2
randomly selected questions out of the 8. If the order of the questions is not important, how many
different unique question papers exist?
W​

Answer 1

Answer:

56 Different Unique Question paper will exist

Step-by-step explanation:

Let's look at this from a different perspective, so here we go

We know that,

There are 8 total Questions out of which 2 are selected,

here the question order is not considered

Thus,

let's take this in terms of coordinate system,

Let the x coordinate be the Question numbers from 1 to 8 and y coordinate be the other possible values.

Now let's take x = 1 (Question 1)

then possible values of y = 2, 3, 4, 5, 6, 7, 8

(Remember y can't be 1 because logically in an exam a Question can't be repetitive)

So, unique Question papers with Question 1 is:-

(1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8)

Similarly,

x = 2

possible values for y = 1, 3, 4, 5, 6, 7, 8

So, unique Question papers with Question 2 is:-

(2,1), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)

So, when x = 1, number of values for y = n(y) = 7

also, when x = 2, n(y) = 7

Similarly

x goes to 8, so total possible Unique will be 7 × 8 = 56

If you want me to write the whole solution, below is everything.....

(1,2), (1,3), (1,4), (1,5), (1,6), (1,7), (1,8)

(2,1), (2,3), (2,4), (2,5), (2,6), (2,7), (2,8)

(3,1), (3,2), (3,4), (3,5), (3,6), (3,7), (3,8)

(4,1), (4,2), (4,3), (4,5), (4,6), (4,7), (4,8)

(5,1), (5,2), (5,3), (5,4), (5,6), (5,7), (5,8)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,7), (6,8)

(7,1), (7,2), (7,3), (7,4), (7,5), (7,6), (7,8)

(8,1), (8,2), (8,3), (8,4), (8,5), (8,6), (8,7)

Now, since Order of Questions are not considered, If you count all of them, they will add upto 8 × 7 = 56

Thus, 56 Different Unique Question paper will exist when order is not considered.

Hope it helped and you understood it........All the best