Permutation and combinations

Asked by  | 20th Mar, 2009, 10:23: AM

Expert Answer:

the number of line segments  is obtained by  selecting 2 points out of n.

This can be done inC(n.2) ways.

So total number of line segments=C(n,2)

 but out of these n are thee sides, so  remaining have to be diagonals.

So,

 the number of diagonals

=C(n,2)-n

Another way

one point canbe joined with other n-1 points by n-1 line segments.But when you count the total number of line segments, we have to take into consideration that one line segment gets counted twice( like A  to B and  B to A )So we need to divide the total number by 2.

so to total line segments =n(n-1)/2

from this reduce the n line segments which are the sides , so the number of diagonals={n(n-1)/2]-n

Answered by  | 20th Mar, 2009, 12:09: PM

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