Permutations and Combinations · Mathematics · NDA

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 th...

A triangle $PQR$ is such that 3 points lie on the side $PQ$, 4 points on $QR$ and 5 points on $RP$ respectively. Triangles are constructed using these...

If $26! = n8^k$, where $k$ and $n$ are positive integers, then what is the maximum value of $k$?

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?

What is the number of different matrices, each having 4 entries that can be formed using 1, 2, 3, 4 (repetition is allowed)?

If 1! + 3! + 5! + 7! + ... + 199! is divided by 24, what is the remainder?

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

If H is the Harmonic Mean of three numbers 10C4, 10C5, and 10C6, then what is the value of $\frac{270}{H}$ ?...

 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 ? 

Consider the following statements : 1. (25)! + 1 is divisible by 26 2. (6)! + 1 is divisible by 7 Which of the above statements is/are correct ?&nb...

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

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 follow...

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 ?

If the sum S is divided by 8, what is the remainder ?  

If the sum S is divided by 60, what is the remainder ?

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 i...

How many 4-letter words each of two vowels and two consonants with or without meaning, can be formed ?

How many 8-letter words with or without meaning, can be formed such that consonants and vowels occupy alternate positions?

How many 8-letter words with or without meaning, can be formed so that all consonants are together?

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?

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

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 ?

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

What is the value of 2(2 × 1) + 3(3 × 2 × 1) + 4(4 × 3 × 2 × 1) + 5(5 × 4 × 3 × 2 × 1) + ...................

Consider the following statements: 1. $\frac{n!}{3!}$ is divisible by 6, where n > 3 2. $\frac{n!}{3!}+3 $ is divisible by 7,...

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