IIT JEE , AIEEE Forum - Mathematics , Algebra - fast EXPLANATION plzz--perm&comb question

warrior

20 students are sitting at a round table one has to select 5 of them so that no 2 of the selected students are consecutive. no.of ways of selecting students=

ans:(13P5)/36

warrior

explanation req..anyone plz reply

nadeemoidu

I think the answer given is for selecting 6 students , so that 's the solution I will be giving.

consider the no. of gaps ( students) in between 2 chosen students. let them be x₁, x₂, .. x₆.
total no. of such gaps = 20-6 = 14

Therefore x₁ + x₂ + x₃+ x₄ + x₅ + x₆= 14

the no. of non-zero solutions of this equation is ^{( 14-1 )} C_{( 6 - 1)} = ¹³C₅

now the first person can be chosen in 20 ways. and it does not matter which of the 6 students in the final answer is the first student .

So the final answer is 20 ¹³C₅ /6 = 20 ¹³P₅ / 6! = ¹³P₅ /( 6 x 3x2) = ¹³P₅/ 36

puneet

hii

i think i agreee with the reply .. just think of it as if u fixed one position out of the 20 n thn revolved around it ..

well done dear frnd .. good reply

cheers

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