If two different numbers are to be selected from set {1, 2,

Question

. If two different numbers are to be selected from set {1, 2, 3, 4, 5, 6}, what is the probability that the sum of two numbers is a perfect square number?
A. 1/2
B. 1/3
C. 1/9
D. 2/9
E. 4/9

here what confuses me is , in the total poss cases, do we take ,for eg 1,3 and also along with that 3,1 or should they be considered only once?

kapilnegi · Answer

Here perfect squares can be either 4 or 9.

4 = 3+1 or 1+3 (2 ways)
9 = 3+6 or 6 +3 (2 ways)
= total 4 ways

Total ways of selecting to numbers = 6 *6 = 36 ways

Required probabilty = 4/36 = 1/9

arjtryarjtry · Answer

what abot 4,5 and 5,4?
also total ways of selecting two nos. from 6 is 6c2 rite?

zoltan · Answer

We have 15 possible option and 5 good option. Probability=5/15=1/3

arjtryarjtry · Answer

how 5 good option? it shud be 6 rite?

zoltan · Answer

I think we have 5 good options: (1,3) (2,6) (3,5) (3,6) (4,5)

I hpe these are the perfect squere numbers: 4, 8, 9, ...

I am not sure, may be I am not correct.

IanStewart · Answer

2^2 = 4 and 3^2 = 9 are the only perfect squares we can get as a sum of two numbers from the set. Note that 8 is not a perfect square (8 is a cube, however).

Now, we can either assume order matters, or assume it doesn't- we just need to be consistent. If order matters, there are 6*5 = 30 different pairs of numbers we can choose. Again, if order matters, we can get squares in the following ways:
1,3
3,1
3,6
4,5
5,4
6,3

So the probability should be 6/30 = 1/5. That isn't among the answer choices- where is the question from?

hi0parag · Answer

number of ways that you can select 2 numbers out of 6 would be  6 C 2 =15 ways
favourable outcomes are {1,3}, {4,5}, & {3,6} = 3 ways

hence the probability would be 3/15=1/5 (well it is not one of the options!!!)

zoltan · Answer

hi0parag,

Thank you for correcting my mistake.

rahulgoyal1986 · Answer

Wrong Question.

The answer is 1/5

If two different numbers are to be selected from set {1, 2,

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