Start learning →

JEE Main Permutations and Combinations — practice questions

Explore 30 free Permutations and Combinations questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Permutations and Combinations with Quill →

Permutations and Combinations questions and exercises with answers

Showing questions 1–30 of 30.

The value of $5!$ is:Read the answer and worked solution →The number of ways to arrange $n$ distinct objects in a row is:Read the answer and worked solution →How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?Read the answer and worked solution →In how many ways can a committee of $3$ persons be chosen from a group of $10$ people?Read the answer and worked solution →An arrangement in a definite order of a number of objects is called a:Read the answer and worked solution →In a combination, the order of the chosen objects is:Read the answer and worked solution →The multiplication principle is also known as the fundamental principle of:Read the answer and worked solution →The notation n factorial represents the product of the first n:Read the answer and worked solution →Zero factorial is defined as which value?Read the answer and worked solution →The principle for two events can be generalised to how many events?Read the answer and worked solution →If one event can occur in m ways and then another in n ways, the total is:Read the answer and worked solution →With 3 pants and 2 shirts, how many different pant and shirt pairs are there?Read the answer and worked solution →Sabnam has 2 school bags, 3 tiffin boxes and 2 water bottles. How many combinations?Read the answer and worked solution →A number lock has 4 wheels, each labelled with how many digits?Read the answer and worked solution →The lock opens only if the 4 digits are arranged in a sequence with no:Read the answer and worked solution →In the word ROOT, why are the letters not all treated as different?Read the answer and worked solution →Listing every arrangement by hand is rejected as a method because it is:Read the answer and worked solution →Choosing a 2 player team from X, Y and Z gives how many possible teams?Read the answer and worked solution →A selection of 3 different objects taken 2 at a time is called a:Read the answer and worked solution →Twelve people each shake hands with all the others. Order of the pair is:Read the answer and worked solution →A team of 5 with at least 3 girls cannot be all girls. Why not?Read the answer and worked solution →Five factorial can be rewritten as five times which quantity?Read the answer and worked solution →Permutation or combinationRead the answer and worked solution →Count the waysRead the answer and worked solution →Type the counting termRead the answer and worked solution →Which count does it needRead the answer and worked solution →One word is wrongRead the answer and worked solution →Permutation and combinationRead the answer and worked solution →Spot the false statementRead the answer and worked solution →Order the counting build upRead the answer and worked solution →

Worked practice questions

The value of $5!$ is:

  1. $120$
  2. $60$
  3. $720$
  4. $25$
Show answer and solution

Correct answer: A. $120$

Factorial definition: $n! = n \times (n-1) \times (n-2) \times \ldots \times 1$. $5! = 5 \times 4 \times 3 \times 2 \times 1 = 120$. Quick reference: $4! = 24$, $5! = 120$, $6! = 720$ (option D is $6!$, not $5!$). Factorials grow fast.

Open this question →

The number of ways to arrange $n$ distinct objects in a row is:

  1. $2^n$
  2. $n$
  3. $n!$
  4. $n^2$
Show answer and solution

Correct answer: C. $n!$

Arrangements of $n$ distinct objects in a row: $n$ choices for the first position then $n-1$ for the second, $n-2$ for the third, etc. By the multiplication principle: $n \times (n-1) \times \ldots \times 1 = n!$ For 5 books on a shelf: $5! = 120$ arrangements. For 10 students in a line: $10! = 3,628,800$.

Open this question →

How many different 4-digit numbers can be formed using the digits $1, 2, 3, 4, 5$ without repetition?

  1. $24$
  2. $120$
  3. $20$
  4. $625$
Show answer and solution

Correct answer: B. $120$

We need to arrange 4 digits chosen from 5 distinct digits with no repetition. That's $^5 P_4$: $^5 P_4 = \dfrac{5!}{(5-4)!} = \dfrac{120}{1} = 120$. Alternative count by positions: 5 choices for the thousands digit then 4 for hundreds, then 3 for tens, then 2 for units. $5 \times 4 \times 3 \times 2 = 120$ ✓. Option B (625) would be allowed repetition: $5^4 = 625$. Option C is just $4!$ ignoring the choice of digits to use.

Open this question →

How to practise

  1. Choose a Permutations and Combinations question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Permutations and Combinations practice for JEE Main. Read explanations as you go. No signup form needed to start.

Practise Permutations and Combinations →

More Mathematics topics

Statistics and ProbabilityDeterminantsVector Algebra and 3D GeometryContinuity, Differentiability & DerivativesDifferential EquationsIntegrals and ApplicationsMatrices and DeterminantsRelations, Functions & Inverse Trigonometry