Quote:
One qn from P&C
A student has to answer 9 qns out of 12 qns in a qn paper such that he has to answer atleast 3 qns from the first 4 qns . In how many ways can he do this ?
My Soln...
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He can choose the 3 qns out of the first 4 in 4C3 ways ...
and the qns left out now are 9 and he has to answer any 6 of those in 9C6 ways...
Therefore number of ways = 4C3 * 9C6
= 4 *84
= 336
Soln Given ...
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Case 1 : He attempts 3 qns out of the first 4 and the other 6 qns from the rest
No of ways = 4C3 * 8C6
Case 2: He attempts all the 4 qns out of the first 4 qns and the other 5 from the rest
No of ways = 4C4 * 8C5
Total no of ways = 4C3*8C6 + 4C4*8C5
= 4*28 + 56
= 168
Which soln is correct and why ?? What's the diff between the both of them ??
Thanks in advance
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hi,
lemme try...
this one was really interesting one..puzzled me for some time
tried out a simplified version of the problem to find the PROBLEM..
the second soln. given is right.
and the root cause of the mistake in ur soln. is that in it
the selections are not exclusive ...i.e, there are repetitons...
thats why ur getting a higher value for the answer..
for eg..
supose in the prob ...say a,b,c,d,e,f,g,h,i,j,k,l are the 12 answers..
now u select 3 out of the first 4...
ie abc,bcd,acd or abd ...now from the remaining nine ur selecting 6...
let the initial selection be abc ...
from the remaining u r selcting defghi ..so ur full selection becomes..
abcdefghi...
now for another initial selection
say abd ...ur remaining selction cud be cefghi =>totally abcdefghi
both selections are the same...but as per ur soln,these will get get counted as 2.hence the error...
if still not clear try the same problem as
3 out of 4 qs to be answered and atleast 1 from first 2...ull see wht im tying to xplain..
hope my xplanation made some sense...
MrAndy