Lakshya NDA

Paper I — Mathematics

Permutations and Combinations

Exam-focused notes, visual explanation, traps, revision sheet and every mapped past NDA question.

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Core5 mapped NDA questions

Build the idea

Build exam-ready understanding by connecting the core idea, formulas or facts, worked example and previous NDA questions. Focus on why each rule works, then test it under timed conditions.

Concept

Permutations count ordered arrangements; combinations count unordered selections. The fundamental counting principle (multiply the number of choices at each stage) underlies both.

Watch carefully for restrictions, repetition and whether order matters.

Key Points & Formulas

  • nPr = n!/(n−r)! (arrangements of r out of n).
  • nCr = n!/[r!(n−r)!] (selections of r out of n).
  • nCr = nC(n−r); nC0 = nCn = 1.
  • Arrangements of n objects with repeats p,q,…: n!/(p! q! …).

Worked Example

Q. In how many ways can a committee of 3 men and 2 women be chosen from 6 men and 4 women?

Choose 3 men: 6C3 = 20. Choose 2 women: 4C2 = 6.

By the counting principle, total = 20 × 6 = 120.

Common traps

  • Reading the prompt too quickly and missing a qualifier.
  • Memorising the result without checking when it applies.
  • Skipping units, signs, chronology or the final reasonableness check.

NDA shortcuts

  • State the governing rule before substituting values.
  • Eliminate impossible options before doing full calculation.

One-screen revision sheet

Recall before you practise

  • Core definition
  • Most-used rule
  • One representative example

Past-paper bank

Practise every mapped question

5 NDA questions

Choose an answer before the solution appears. Option order is mixed automatically.

Question 1

NDA Practice 2026

The number of distinct arrangements of the letters of the word CAT\text{CAT} is

Question 2

NDA I 2025

What is the number of selections of at most 3 things from 6 different things?

Question 3

NDA II 2024

How many 4-digit numbers are there having all digits as odd?

Question 4

NDA I 2024

How many four-digit natural numbers are there such that all of the digits are even?

Question 5

NDA I 2024

A man has 7 relatives (4 women and 3 men). His wife also has 7 relatives (3 women and 4 men). In how many ways can they invite 3 women and 3 men such that 3 of them are the man's relatives and 3 are his wife's relatives?