Algebra

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18 Mar 2012 23:36:01 IST
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Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Algebra

How many ways can 4 prizes be given away to 3 boys, if each boy is eligible for all the prizes????



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kartikAIR1's Avatar

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18 Mar 2012 23:55:50 IST
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 63


Hot goIITian

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19 Mar 2012 00:21:57 IST
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are u sure... i think its 64..
kartikAIR1's Avatar

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19 Mar 2012 00:33:02 IST
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 I got 99


Hot goIITian

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19 Mar 2012 00:34:32 IST
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i got it 64.... but given answer is 81.... can some1 explain whats the exact answer??
kartikAIR1's Avatar

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19 Mar 2012 00:40:38 IST
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 I made three groups of prizes, 

 

grp 1 = (2,1,1) =  3C14C22C1

grp 2 = (3,1,0) = 3C12C14C3

grp 3 = (4,0,0) = 3C1

grp 4 = (2,2,0) = 3C12C14C2

 

adding = 36 + 24 + 3 + 36 = 99

 

typing each letter on keyboard really sucks............


Hot goIITian

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19 Mar 2012 01:00:20 IST
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Hey I understood the ansswer is 81... You take 1 prize 1st... you can give that prize to 3 students in 3 ways... so u can give the 2nd prize in 3x3 ways... i.e. 9.... hence u can give 4 prizes in 3x3x3x3 i.e. 81 ways...
kartikAIR1's Avatar

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19 Mar 2012 01:13:26 IST
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 yup, 

I got it, it was easy, 

place 4 prizes stationary on table,

now each prize can be own by single person,

 

so.

prize 1 can be taken by either of  3 students i.e   3C1,

 

similarly,

for prize 2,3,4 i.e. 3C1

 

Total = 3C1 3C13C13C1 = 81


New kid on the Block

Joined: 16 Nov 2011
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19 Mar 2012 07:30:10 IST
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4c4 + 4c3.4c1.4c0+ 4c2.4c1.4c1 is the answer

 


Hot goIITian

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19 Mar 2012 10:01:35 IST
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The 4 prizes can be distributed to 3 boys in 


Cool goIITian

Joined: 19 Mar 2012
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19 Mar 2012 12:38:54 IST
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simple 1...its 3^4...n d answr is simply 81.....!!


Hot goIITian

Joined: 3 Feb 2012
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19 Mar 2012 23:47:15 IST
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plzz.. can u explain me this combinations method... i dont kno anything about it..... i do all sums fully logically taking cases which takes a long time.... if u dun mind can u teach me how to do sums with C method....

Cool goIITian

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20 Mar 2012 00:00:02 IST
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c its quite simple.....m xplaining it logically.....listen first step is 2 make a situation unbiased.....it means.....we can't ask each boy....dat he want how many prizes....does he want.....as he will select all of dem and d situation will bcum biased....therefore v will ask d prizes.....!! therefore....d first prize can select any 1 out of 3 boys dat is 3c1....similarly...can also select and one out of 3 boys i.e...3c1...similarly...3rd and 4th prize...therefore....total ways r...3c1 * 3c1 * 3c1 * 3c1......i.e 3*3*3*3=3^4=81 ways...is it clear...???

Cool goIITian

Joined: 19 Mar 2012
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20 Mar 2012 00:01:24 IST
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sorry.....lill mistake...cut does he want...frm here...:P

Cool goIITian

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20 Mar 2012 00:04:51 IST
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c its quite simple.....m xplaining it logically.....listen first step is 2 make a situation unbiased.....it means.....we can't ask each boy....dat how many prizes....does he want.....as he will select all of dem and d situation will bcum biased....therefore v will ask d prizes.....!! therefore....d first prize can select any 1 out of 3 boys dat is 3c1....similarly..2nd prize...can also select and one out of 3 boys i.e...3c1...similarly...3rd and 4th prize...therefore....total ways r...3c1 * 3c1 * 3c1 * 3c1......i.e 3*3*3*3=3^4=81 ways...is it clear...???

Hot goIITian

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21 Mar 2012 21:01:47 IST
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yeah... thank u so much... best of luck for ur jee....

Cool goIITian

Joined: 19 Mar 2012
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22 Mar 2012 19:33:17 IST
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WeLcUm...!!! PlZrR...! ^_^



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