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NDA 2021 Maths · Mathematics · Permutations and Combinations · medium

^nPr=^nCr / r!. 2. The number of circular arrangements of n distinct objects is n!.

Single correct option

Which of the statements is/are correct? 1. nPr=nCr / r!^nP_r={}^nC_r\,/\,r!. 2. The number of circular arrangements of nn distinct objects is n!n!.
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
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Answer: (D) Neither 1 nor 2

The correct relation is nPr=nCr⋅r!^nP_r={}^nC_r\cdot r!, so statement 1 is wrong. Circular arrangements of nn distinct objects number (n−1)!(n-1)!, so statement 2 is wrong. Neither is correct.
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Original question written in the NDA 2021 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