Testbook [Counting]

Question

I applied the formula for onto function and got 36. How are they getting 360?

Comments

Is here concept of onto required? Each ring can go to any finger and hence, 3⁴ ways.

Answer 1

Totally 4 rings and 3 fingers 

Each ring can be worn to any of the 3 fingers 

Hence there are 3⁴

Comments

Thanks @Prajwal

I think I have got my mistake.

3 fingers can be chosen from 5 in $\binom{5}{3}$ ways = 10.

Once chosen, 4 distinct rings can be distributed in 3 fingers in $3^{4} - \binom{3}{1}\left ( 3-1 \right )^{4} + \binom{3}{2}\left ( 3-2 \right )^{4}$ ways = 36.

Total 360 ways.

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Nice that you have found out another solution

But i don't think we should consider 5 fingures since for this context they have externally mentioned 3 fingers

So choosing 3 from 5 is out of the context of this problem i feel, what do you say?

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You are absolutely correct. Further, they havent mentioned if the rings were worn on the fingers of one hand. They could well be worn on both hands, so we dont know from how many fingers, 3 fingers are to be chosen.

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How are you calculating answer this way???? I think you are just trying to set formulas to get your answers. Answer should be 3⁴ becuase each ring has 3 choice.

http://math.stackexchange.com/questions/437152/prove-that-the-number-of-ways-to-put-n-distinct-balls-into-n-distinct-boxes

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@Prajwal. Answer is wrong.

Consider there are 2 rings in 1 finger. WHen you perform 4!,  its possible that same 2 rings come to same finger but the order in which they are inserted into the finger different. Thats not valid counting.

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3⁴ is right answer.

If onto is required, 4C2 * 3! = 36  but nothing is mentioned about onto and hence, we cant assume.

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@Sushant

I thought that we apply onto concept, when 'n' distict items are to be distributed among 'r' different groups. Why is it not so here?

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They should explicitly mention "Each finger must have atleast 1 ring"

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Spot on!! Missed this point... Thanks a lot

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Sushant, Thanks for correcting. I didn't see about the order of the ring worn .3^4 looks correct to me now.

Rahul Jain, I didn't try set any formulas here, what came to mind while seeing the question i wrote in the ans may be i didn't see the problem in that perspective .you have all the right to agree or disagree with my ans and correct it if you found wrong.

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No offence bro, I just disagreed with your answer☺

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As i said you have complete freedom of disagreeing with any ones opinion!!