IIT JEE , AIEEE Forum - Mathematics , Algebra - Contest [swordfish #2]: Find ways to select people on circular table

wiz_naf

Total No. of arrangements = 16!* 8!

iit2007

ans 16*13*11*9*7*6*5*3*1

archit

Mahender

this ans can be solve only with the help of expert

santosh_0804

since 16 people

2 must be selected

it is nothig but arranging 2 in 14 people

hence 14 gaps

so selecting 14 people and arranging in table

(16c2)*13!

hence 14 gaps and 2 to arrange

14p2=91

answer=(14p2)*13!*(16c2)

mohitbhatia

2 * 8

C = 16

7

piyushmalik

PERMUTATION IS NOT REQUIRED HERE,ONLY COMBINATION CONCEPT IS TO BE USED SINCE WE HAVE TO SELECT 7 PEOPLE AND NOT TO ARRANGE THEM.

TO SELECT 7 PEOPLE OUT OF 16 SO THAT NO TWO ARE COMSECUTIVE IS = 9

C

7

rahul_c

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

tejal_iitian

there are 16 people and 7 have 2 b seleced

there r 9 people left and as the 7 people have not to sit consecutivel so choices

10p7 (as 10 gaps)

10!/3!

604800.

rahulprakash

seven people can sit in 8 places as no two persons should be consecutive.
no. of ways=8C7*7P7*2

tejal_iitian

¹⁰C₇

120

malay

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??

akshat_spike2002

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 * ⁷C_{6 =} 112

001sri

9C7 must b the answer .we have 16 seats around a table(round).

now it can b thought of as we have to select 7 seats out of the 9 gaps created by seating the remaining 9.

here permutation is not required as persons r fixed on their seats.

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