The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$ sided regular polygon is

66

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30

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24

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15

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Solution

The correct option is D $15$
The first vertex can be choosed in $12$ ways and diagonally opposite to it is $1$ vertex. Now for $3 r d$ vertex we have $10$ choices and for $4 t h$ $1.$
However, each rectangle is counted $8$ times.
$∴$ No. of ways $= \frac{12 \times 1 \times 10 \times 1}{8}$ $= 15$ ways.
Hence, the answer is $15.$

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The number of rectangles that can be obtained by joining four of the twelve vertices of a 12 sided regular polygon is

The correct option is D 15The first vertex can be choosed in 12 ways and diagonally opposite to it is 1 vertex. Now for 3rd vertex we have 10 choices and for 4th 1.However, each rectangle is counted 8 times.∴ No. of ways =12×1×10×18 =15 ways.Hence, the answer is 15.

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$ sided regular polygon is