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Algebra
18 Nov 2006 03:11:18 IST
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Avirup Dasgupta
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11 Jan 2008 22:58:49 IST
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This is easy.
Total number of ways of selecting 7 people = 16c7
From this we have to subtract number of ways all three are consecutive =16 and also the number of ways inwhich two are consecutive = 16x 12c1
Therefore the final answer is = 16c7 - 16 - 16x12c1.
Got it???
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27 Jan 2008 00:38:38 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
27 Jan 2008 00:43:50 IST
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Ways 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
9 Mar 2008 17:36:07 IST
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My answer is same as the winner's answer but i 'll try to explain my method in a much simpler way.
consider the no. of gaps ( students) in between 2 chosen students. let them be x1, x2, .. x7.
total no. of such gaps = 16 - 7 =9
Therefore x1 + x2 + x3 + x4 + x5 + x6 +x7 = 9
the no. of solutions of this equation is ( 9-1 ) C ( 7 - 1) = 8C6
now the first person can be chosen in 16 ways. and it does not matter which of the 7 students in the final answer is the first student .
So the final answer is 16 8C6 / 7
consider the no. of gaps ( students) in between 2 chosen students. let them be x1, x2, .. x7.
total no. of such gaps = 16 - 7 =9
Therefore x1 + x2 + x3 + x4 + x5 + x6 +x7 = 9
the no. of solutions of this equation is ( 9-1 ) C ( 7 - 1) = 8C6
now the first person can be chosen in 16 ways. and it does not matter which of the 7 students in the final answer is the first student .
So the final answer is 16 8C6 / 7
18 Apr 2011 08:25:10 IST
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well number of ways of arranging 16 people in a circle is (16-1)! or 15!. so first person can be seated in any 16 seats the next can sit on any 13(since he should not be seated on either side of the first person), then the third can sit in any 11 seats ........ and so on. so total number of ways comes out to be 16*13*11*9*7*5*3 that is 2162160 answer.
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