List of top Mathematics Questions on permutations and combinations

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

If all the words with or without meaning made using all the letters of the word "KANPUR" are arranged as in a dictionary, then the word at 440^th position in this arrangement is:

The number of 6-letter words, with or without meaning, that can be formed using the letters of the word MATHS such that any letter that appears in the word must appear at least twice, is $ 4 \_\_\_\_\_$.

If the number of seven-digit numbers, such that the sum of their digits is even, is $ m \cdot n \cdot 10^a $; $ m, n \in \{1, 2, 3, ..., 9\} $, then $ m + n $ is equal to

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1’s and exactly three 2’s, is equal to:

The number of four digit even numbers that can be formed using the digits 0, 1, 2 and 3 without repetition is:

Number of all possible ways of distributing eight identical apples among three persons is

Number of all possible words (with or without meaning) that can be formed using all the letters of the word CABINET in which neither the word CAB nor the word NET appear is

There are 15 stations on a train route and the train has to be stopped at exactly 5 stations among these 15 stations. If it stops at at least two consecutive stations, then the number of ways in which the train can be stopped is

There are 6 boys and 4 girls. Arrange their seating arrangement on a round table such that 2 boys and 1 girl can't sit together.

How many different 4-letter words can be formed from the letters of the word "BINARY" without repetition?

Group A consists of 7 boys and 3 girls, while group B consists of 6 boys and 5 girls. The number of ways, 4 boys and 4 girls can be invited for a picnic if 5 of them must be from group A and the remaining 3 from group B, is equal to:

In how many ways can a chairperson, a secretary, and a treasurer be chosen from a group of 10 people, if each person can hold only one position?

All letters of the word `AGAIN' are permuted in all possible ways, and the words so formed (with or without meaning) are written as in a dictionary. Then the $50^{th}$ word is

The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders, and 4 wicket-keepers by selecting at least 4 batsmen, at least 3 bowlers, at least 2 all-rounders, and only one wicket-keeper is

The number of ways of forming the ordered pairs (p, q) such that p>q by choosing p and q from the first 50 natural numbers is:

If all possible 4-digit numbers are formed by choosing 4 different digits from the given digits $ 1, 2, 3, 5, 8 $, then the sum of all such 4-digit numbers is:

If $ {}^9P_3 + 5 \cdot {}^9P_4 = {}^{10}P_r $, then the value of $ 'r' $ is:

How many 4-digit numbers (between 1000 and 9999) can be formed using the digits $2, 3, 5, 7, 8$ such that:

Each number contains both $3$ and $7$ exactly once,
No digit is repeated.

The number of ways of arranging 3 red, 2 white, and 4 blue flowers of different sizes into a garland such that no two blue flowers come together is:

Let $ S $ be the set of all seven-digit numbers that can be formed using the digits 0, 1 and 2. For example, 2210222 is in $ S $, but 0210222 is NOT in $ S $.
Then the number of elements $ x $ in $ S $ such that at least one of the digits 0 and 1 appears exactly twice in $ x $, is equal to __________.

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is:

The value of the expression $ {}^{47} C_4 + \sum_{j=1}^{5} {}^{52-j} C_3 $ is:

There are 12 points in a plane in which 5 are collinear such that no three of them are in a straight line. Then the number of triangles that can be formed from any 3 vertices from 12 points.