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Radon222 (166)

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\text{ The sum } \displaystyle\sum_{i=0}^{m} .(^{10}C_i).(^{20}C_{m-i}) \\ \\    (where, ^pC_q = 0 \text{ if } p<q) \text{is maximum,when m is??}

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sandeepramesh (1247)

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m>10 is useless
so m = 10 :D
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Radon222 (166)

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Wrong !

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sandeepramesh (1247)

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then tell me the answer!!! There's no other go man :D
 
m cannot be > 10, atleast do you agree on that???
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sboosy (3063)

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Now we have 10Ci and 20Cm-i . of all the values of combinations of 10 10C5 is maximum ,similarly 20C10 is maximum ..now multipying these together wud produce a high value . thus both shud be attained simultaneously
means m-5 = 10
so m = 15 ... thus we end up multiplying the big numbers with their counterparts ..
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sandeepramesh (1247)

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but for m> 10, 1st term becomes 0 accord to how he defined it
 
EDIT: Found the mistake thanx :)
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Radon222 (166)

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Sboosy is right !

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pottermania1990 (342)

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xCy means selecting y objects from x objects

so 10C15 makes no meaning......

so radon tell where my logic is going wrong
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sandeepramesh (1247)

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but he already defined it as 0 :)
 
so that is a valid thing :)
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pottermania1990 (342)

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ohh i dinn c that ..thanks
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pink_ele (1233)

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(1+x)10=10C0+10 C1x?????10C10x10
(1+x) 20=20C0+20 C1x?????20C20x 20
MULTIPLY  DEN EQUATE COEFF OF xr
It?s a common proof dear u must have read
=30C m
Its max for m=15
Cheers !

nobody is wrong
even a stopped clock is right twice a day
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Decoder (454)

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the other..way..
solving the summation u get..

sum { 10Ci . 20Ci } (m-i is same as i as far as values of coeff r concerned)

now solving..
u will get max of 30Cm ..wic happens wen m is 15..

Diamonds r formed under greatest pressures..
so r the champs.


Kriteesh..


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