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Algebra
18 Nov 2006 03:11:18 IST
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mohitbhatia
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26 Dec 2006 12:37:38 IST
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2 * 8
C = 16
7
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29 Dec 2006 15:40:38 IST
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to select 7 people such that none is consecutive would be
First person can occupy any of the 16 chairs
Second person can sit in rest of the 13 chairs
Third in 11, Fourth in 9,Fifth in 7, Sixth in 5 ,proceeding in this way
Therefore total number of ways to sit= 16*13*11*9*7*5*3=2162160
First person can occupy any of the 16 chairs
Second person can sit in rest of the 13 chairs
Third in 11, Fourth in 9,Fifth in 7, Sixth in 5 ,proceeding in this way
Therefore total number of ways to sit= 16*13*11*9*7*5*3=2162160
29 Dec 2006 18:03:11 IST
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Suppose that 7 people are sitting round the table(and these are the chosen people)
Make other seven out of nine left to sit between each two.
One will sit anywhere he want.
For, each place where the last one will sit give a different arrangement.
Hence the answer is four due to circular symmetry.
this is the solution, I hope, if all the people are identical
if all the people are different, then this solution can be extended to C(16,7)*C(9,7)*{C(7,2)+C(7,1)}
Anyone has a doubt??
Make other seven out of nine left to sit between each two.
One will sit anywhere he want.
For, each place where the last one will sit give a different arrangement.
Hence the answer is four due to circular symmetry.
this is the solution, I hope, if all the people are identical
if all the people are different, then this solution can be extended to C(16,7)*C(9,7)*{C(7,2)+C(7,1)}
Anyone has a doubt??
31 Dec 2006 10:15:38 IST
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Since we have to select 7 people out of 16 so that no two are consecutive:-
Suppose we take one and select it as 16C1! Now the two immediate to it can't be selected ! Left are 7 which can be selected as they are alternate! therefore we have to select 6 out of them as we have already selected ONE! therefore 7C6
Answer is 16C1 * 7C6 = 112
21 Jan 2007 22:22:55 IST
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total no of people to be arranged arround a circular table = 16
no. of ways in which remaining 9 people may be arranged = ( 9 - 1)! = 8!
the other 7 persons may be arranged among themselves in 7! ways.
Thus total no. of ways = 8! * 7! = 203212800
7*7!/2!
11 Jan 2008 22:22:19 IST
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since we have to select 7 ppls frm 16 but no consicutives shoul b selected then
lets start this way
consider a person as the head...
now including the head we have 8 members in which no two are consicutive..
there4 the total no. of ways 4 selection of 7 ppl frm 8 is
8c7
now the person just next to the head is excluded in the 1st case ,so now lets count him now and the other 7 ppl who were left before , so now again we have 8 members and no 2 of them are consicutive
again the total no of ways to select 7 ppl frm 8 is
8c7
now the case 1 is independable of the case 2 there4
total no of cases will be
8c7+8c7=2*8c7=2*8c1=16
ans is 16
lets start this way
consider a person as the head...
now including the head we have 8 members in which no two are consicutive..
there4 the total no. of ways 4 selection of 7 ppl frm 8 is
8c7
now the person just next to the head is excluded in the 1st case ,so now lets count him now and the other 7 ppl who were left before , so now again we have 8 members and no 2 of them are consicutive
again the total no of ways to select 7 ppl frm 8 is
8c7
now the case 1 is independable of the case 2 there4
total no of cases will be
8c7+8c7=2*8c7=2*8c1=16
ans is 16
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