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

nadeemoidu

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

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