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NDA 2018 Maths · Mathematics · Permutations and Combinations · medium

A hexagon has exactly 9 diagonals. 2. The number of ways in which 5 persons can be seated around a circular table is 24.

Single correct option

Consider the following statements: 1. A hexagon has exactly 9 diagonals. 2. The number of ways in which 5 persons can be seated around a circular table is 24. Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (C) Both 1 and 2

Diagonals of an nn-gon: (n2)−n=15−6=9\binom n2-n=15-6=9, so statement 1 holds. Circular arrangements of 5 distinct persons: (5−1)!=24(5-1)!=24, so statement 2 holds. Both are correct; the trap is to use 5!=1205!=120 for the circular case.
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Original question written in the NDA 2018 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake