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  • Please,please help me - Permutations and combinations - BITSAT

Let T_{n} be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If T_{n+1}-T_n=10 then the value of n is :

 

 

  • Option 1)

    8

  • Option 2)

    7

  • Option 3)

    5

  • Option 4)

    10

 

Answers (1)

best_answer

As we have learned

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

^{n}c_{r}=\frac{(n)!}{r!(n-r)!}

- wherein

Where 1\leq r\leq n

 

 T_n= ^n C_3 =  no. of selection of 3 vertices out of n vertices 

T_{n+1}-T_n= 10

\Rightarrow ^{n+1}C_3- ^nC_3= 10

\Rightarrow \frac{(n+1)(n)(n-1)}{6}- \frac{n(n-1)(n-2)}{6}= 10

\Rightarrow n{(n+1)\left \{ n+1-n+2 \right \}= 60

n^2-n = 20

\Rightarrow n^2-n - 20 = 0

\therefore n = 5 \: \: or\: \: n= -4

 

 

 

 

 

 

 


Option 1)

8

Option 2)

7

Option 3)

5

Option 4)

10

Posted by

gaurav

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