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Consider the set of numbers $N= 1,2,3,4,5,6,7,8$. Take every distinct two-element subset of $N$ and write down the number that is smaller. For eg, if you take the subset$\left ( 2,5 \right )$, you will write down $2$.

The sum of all the numbers that you write down is ___________.

The possible pairs are (1,2),(1,3),(1,4),(1,5),(1,6),(1,7),(1,8).

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

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

(4,5),(4,6),(4,7),(4,8)

(5,6)(5,7)(5,8)

(6,7),(6,8)

(7,8)

Therefore total sum =(1*7)+(2*6)+(3*5)+(4*4)+(5*3)+(6*2)+(7*1)

=84

(2,3) AND (3,2) ARE THEY SAME???
Yes,because from the subset you have to choose the minimum value only.

But, in the exam how can we differentiate , that we need to take (2,3) only and not (3,2)?

Is there any Hint itself in the Question?

Order

The definition of set states that a "set is an unordered collection of elements. What does this mean about sets C and D, below?

C={10,27,4}D={4,10,27}

Sets C and D are equal because there elements are the same. The only difference is the order, which doesn't matter.

So   84 is correct.

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### 1 comment

Got it !!! Thanks