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NDA 2025 Maths · Mathematics · Permutations and Combinations · easy

Binom nr=binom nn-r 2. ^nPr=r!· ^nCr Which of the statements is/are correct?

Single correct option

Consider the following statements:
1. (nr)=(nn−r)\binom nr=\binom n{n-r}
2. nPr=r!⋅ nCr^nP_r=r!\cdot\,^nC_r
Which of the statements 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

Both are standard results. Choosing rr objects to take is the same as choosing n−rn-r to leave, so statement 1 holds. Statement 2 holds since nPr=n!(n−r)!=r!⋅n!r!(n−r)!^nP_r=\frac{n!}{(n-r)!}=r!\cdot\frac{n!}{r!(n-r)!}: each combination can be arranged in r!r! orders.
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Original question written in the NDA 2025 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