Mathematics Test 100

Result

Mathematics Test 100

Score
-
out of -
Rank
-
out of -

TIME Taken - -

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Weekly Quiz Competition

Question 1
4 / -1

Let the subset S of the set {1,2,3,4,5,6,7,8,9} be randomly formed such that sums of each unordered pair of distinct numbers from S are all different. Then the probability that number of elements in set S is greater than 5 is -

A
0

B
1/8

C
1/10

D
1/20

Solution

Smallest possible sum is 3 & largest possible sum is 17, that gives 15 possible sums from 3 to 17.

If S has '6' elements then it has

⁶C₂ = 15 different sums.

⇒ S contains 3 (1 + 2) also 17 (9 + 8)

But 1 + 9 = 2 + 8

⇒ No 'S' containing 6 elements least.

⇒ Required probability = 0.