List of top Mathematics Questions on Permutation and Combination

A college has 10 basketball players. A 5-member team and a captain will be selected out of these 10 players. How many different selections can be made?
The number of ways by which 6 distinct balls can be put in 5 distinct boxes are
In how many ways can 8 different chocolates be distributed among 5 children such that each can get any number of chocolates (including zero)?
In how many ways can 8 letters be posted in 5 letter boxes.
How many different words can be formed using all the letters of the word TUESDAY such that no two vowels are together?
In how many ways can the word 'ESPECIALLY' be arranged such that the vowels always come together?
How many words can be formed using all the letters of the word TUESDAY such that all the vowels are together?
The number of words that can be formed by using all the letters of the word 'MISSISSIPPI' is
In how many ways can the letters of the word 'PEANUT' be arranged?
There are 23 buses available between Dinu's house and his school. How many ways are possible for Dinu to go from his house to school and return using different buses?
Babita has to go to a party. She decides to wear either a Saree or a dress. If Babita has 5 Sarees and 6 dresses, in how many ways can she choose her outfit?
Ram has 4 formal shirts and 5 formal trousers, in how many ways can he choose his outfit for the interview?
A person has three different bags and four different books. The number of ways, in which he can put these books in the bags so that no bag is empty, is:
A box contains 5 blue, 6 yellow and 4 red balls. The number of ways, of drawing 8 balls containing at least two balls of each colour, is :
The number of ways of forming a queue of 4 boys and 3 girls such that all the girls are not together, is:
The number of seven-digit numbers that can be formed by using the digits \(1,2,3,5,7\) such that each digit is used at least once, is:
If \( \alpha, \beta \) are roots of the equation \( 12x^2 - 20x + 3 = 0 \), \( \lambda \in \mathbb{R} \). If \( \frac{1}{2} \leq |\beta - \alpha| \leq \frac{3}{2} \), then the sum of all possible values of \( \lambda \) is:
In how many ways can the word ‘ESPECIALLY’ be arranged such that the vowels always come together?
What shall be the arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421 including itself?
How many four digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, 6, such that no digit is used more than once and 0 does not occur in the left-most position?
There are 6 boxes numbered 1, 2, 3, 4, 5, 6. Each box is to be filled up either with a red or a green ball in such a way that at least 1 box contains a green ball and the boxes containing green balls are consecutively numbered. The total number of ways in which this can be done is:
In how many ways can the letters of the word MATHEMATICS be arranged so that all the vowels always come together?
From a group of 7 men and 6 women, 5 persons are to be selected so that at least 3 men are on the committee. In how many ways can this be done?
The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together is:
In a group of 3 girls and 4 boys, there are two boys \( B_1 \) and \( B_2 \). The number of ways in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but \( B_1 \) and \( B_2 \) are not adjacent to each other, is: