NDA PYQ Permutation and Combination - Chapter-wise Questions with Solutions

About Permutation and Combination PYQs

Permutation and Combination has 129 previous year questions in the Quantrex Academy NDA Mathematics bank. The 129 questions in this list come from NDA (129), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Permutation and Combination PYQs with Solutions

About Permutation and Combination PYQs

Questions by year (this list)

Permutation and Combination questions with solutions

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that

How many numbers greater than 1000 can be formed using the digits 0 , 1 , 2 and 3 (repetition of digits is not allowed) ?

What is the maximum number of points of intersection of 5 circles ?

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that

If n= ^ m C_2 then what is ^ n C_2 equal to ?

Passage: A 4-digit number is selected at random formed by using the digits 0 , 1 , 2 , 3 and 4 (where repetition of digits is not allowed). Question: What is the probability that

How many 4-digit numbers that are divisible by 4 can be formed using the digits 1, 2, 3 and 4 (repetition of digits is not allowed)?

For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many quadrilaterals can be formed by joining these points?

Let y = x! and z = (2x)! . If (z/y) = 120 , then what is the value of (3x)! ?

In how many ways can the letters of the word DELHI be arranged keeping the positions of vowels and consonants unchanged?

How many sides are there in a polygon which has 20 diagonals?

How many 7-letter words (with or without meaning) can be constructed using all the letters of the word CAPITAL so that all consonants come together in each word?

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

For the following two (02) items: There are 8 points on a plane out of which 4 points are collinear. How many triangles can be formed by joining these points?

Let n be a natural number. The number of consecutive zeros at the end of the expansion of n! is exactly 2. How many values of n are possible?

If the number of selections of r as well as (n+r) things from 5n different things are equal, then what is the value of r ?

What is the number of positive integer solutions of x + y + z = 5 ?

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

In how many ways can the letters of the word INDIA be permutated such that in each combination, vowels should occupy odd positions?

The letters of the word EQUATION are arranged in such a way that all vowels as well as consonants are together. How many such arrangements are there?

The letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?

Three perfect dice D_1, D_2 and D_3 are rolled. Let x, y and z represent the numbers on D_1, D_2 and D_3 respectively. What is the number of possible outcomes such that x < y < z ?

What is the sum of all four digit numbers formed by using all digits 0,1,4,5 without repetition of digits?

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 so that 3 of them are man's

If 26!= _n 8^k , where k and n are positive integers, then what is the maximum value of k ?

A triangle PQR is such that 3 points lie on the side PQ, 4 points on QR and 5 points on R P respectively. Triangles are constructed using these points as vertices. What is the

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

Four digit numbers are formed by using the digits 1,2,3,5 without repetition of digits. How many of them are divisible by 4 ?

In how many ways can a student choose (n-2) courses out of n courses if 2 courses are compulsory (n > 4) ?

What is the maximum number of points of intersection of 10 circles?

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that all three boys sit together?

Three boys, P, Q, R an three girls S, T, U are to be arranged in a row for a group photograph. What is the probability that no two girls sit together?

Paragraph: Consider the sum S=0!+1!+2!+3!+4!+…+100!34 Question: If the sum S is divided by 8 , what is the remainder?

Let x be the number of permutations of the word 'PERMUTATIONS' and y be the number of permutations of the word 'COMBINATIONS'. Which one of the following is correct?

5 - digit numbers are formed using the digits 0,1,2,4,5 without repetition. What is the percentage of numbers which are greater than 50,000 ?

m parallel lines cut n parallel lines giving rise to 60 parallelograms. What is the value of (m+n) ?

What is the number of 6 digit numbers that can be formed only by using 0,1,2,3,4 and 5 (each once); and divisible by 6 ?

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

If different permutations of the letters of the word 'MATHEMATICS' are listed as in a dictionary, how many words (with or without meaning) are there in the list before the first

Paragraph: Consider the word 'QUESTION' : Question: How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?

A box contains 2 white balls, 3 black balls and 4 red balls. What is the number of ways of drawing 3 balls from the box with at least one black ball?

Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed so that all consonants are together?

Paragraph: Consider the word 'QUESTION' : Question: How many 8 -letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

How many odd numbers between 300 and 400 are there in which none of the digits is repeated?

How many permutations are there of the letters of the word 'TIGER' in which the vowels should not occupy the even positions?

If C(3 n, 2 n)=C(3 n, 2 n-7) , then what is the value of C(n, n-5) ?

What is the maximum value of n such that 5^n divides (30! +35 !), where n is a natural number?

In how many ways can a team of 5 players be selected out of 9 players so as to exclude two particular players?

If C(n, 4), C(n, 5) and C(n, 6) are in AP, then what is the value of n ?

Let S=\ 2,3,4,5,6,7,9\ . How many different 3-digit numbers (with all digits different) from S can be made which are less than 500 ?

Suppose 20 distinct points are placed randomly on a circle. Which of the following statements is/are correct? 1. The number of straight lines that can be drawn by joining any two

Seven white balls and three black balls are randomly placed in a row. What is the probability that no two black balls are placed adjacently?

In how many ways can a team of 5 players be selected from 8 players so as not to include a particular player?

Consider the digits 3,5,7,9 . What is the number of 5 -digit numbers formed by these digits in which each of these four digits appears?

How many 4-letter words (with or without meaning) containing two vowels can be constructed using only the letters (without repetition) of the word 'LUCKNOW'?

Consider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?

How many 5-digit prime numbers can be formed using the digits 1,2,3,4,5 if the repetition of digits is not allowed?

If C(20, n+2)=C(20, n-2) , then what is n equal to?

What is the number of ways in which the letters of the word 'ABLE' can be arranged so that the vowels occupy even places?

What is the maximum number of points of intersection of 5 non-overlapping circles?

What is the number of diagonals of an octagon?

If P(n, r)=2520 and C(n, r)=21 , then what is the value of C(n+1, r+1) ?

What is C(47,4)+C(51,3)+C(50,3)+C(49,3)+C(48,3)+ C (47,3) equal to?

There are 10 points in a plane. No three of these points are in a straight line. What is the total number of straight lines which can be formed by joining the points?

How many three-digit even numbers can be formed using the digits 1,2,3,4 and 5 when repetition of digits is not allowed ?

From 6 programmers and 4 typists, an office wants to recruit 5 people. What is the number of ways this can be done so as to recruit at least one typist?

If n ! has 17 zeros, then what is the value of n ?

If C(20, n+2)=C(20, n-2) , then what is n equal to?

Where A^ is the complement of A . Let x be the number of integers lying between 2999 and 8001 which have at least two digits equal. Then x is equal to

The total number of 5-digit numbers that can be composed of distinct digits from 0 to 9 is

There are 17 cricket players, out of which 5 players can bowl. In how many ways can a team of 11 players be selected so as to include 3 bowlers?

What is the sum of all three-digit numbers that can be formed using all the digits 3,4 and 5 , when repetition of digits is not allowed?

Three dice having digits 1,2,3,4,5 and 6 on their faces are marked I, II and III and rolled. Let x, y and z represent the number on die =I die =II and die -III respectively. What

How many numbers between 100 and 1000 can be formed with the digits 5,6,7,8,9 , if the repetition of digits is not allowed?

What is the number of triangles that can be formed by choosing the vertices from a set of 12 points in a plane, seven of which lie on the same straight line?