Permutation-Combination
Aptitude

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Q.

How many diagonals can be drawn in a pentagon?

 A.

5

 B.

7

 C.

8

 D.

10

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Solution:
Option(A) is correct

A pentagon has $5$ sides. We obtain the diagonals by joining the vertices in pairs.

Total number of sides and diagonals:

$= {^5C_2}$

$= \dfrac{5×4}{2×1}$

$= 5×2$

$= 10$

This includes its $5$ sides also.

⇒ Diagonals $= 10 - 5 = 5$

Hence the number of diagonals,

$= 10 - 5$

$= 5$


(1) Comment(s)


Raj Singh
 ()

From one vertex, you can draw 3 diagonals. From second vertex again you can draw 3 more diagonals. From third vertex again you can draw 3 more diagonals. Overall, you can draw 5x3=15 diagonals in a pentagon.