1. Tardigrade
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  3. Mathematics
  4. There are 20 points lying on a circle, distance between two consecutive points is same. Three points are selected at random. X represents number of ways to select them. Y represents number of ways to select them such that no two adjacent objects are selected and Z represents number of ways to select them such that chosen objects are not diametrically opposite. Which of the following is/are comect?

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Q. There are 20 points lying on a circle, distance between two consecutive points is same. Three points are selected at random. X represents number of ways to select them. Y represents number of ways to select them such that no two adjacent objects are selected and $Z$ represents number of ways to select them such that chosen objects are not diametrically opposite. Which of the following is/are comect?

Permutations and Combinations

Solution:

$ X ={ }^{20} C _3=1140 $
$Y =\frac{20}{3} \times{ }^{16} C _2=\frac{20 \times 16 \times 5}{6}=800$
$Z ={ }^{20} C _3-10 \times 18=1140-180=960 $
$Y \cap Z = Y \text { and } Z \text { both }= Y -10 \times 14=800-140=660$