List of top Mathematics Questions on permutations and combinations

If a polygon has 54 diagonals, find the number of sides of the polygon.
A coach needs to select a \(4\)-player starting lineup from a pool of \(10\) players consisting of:
• \(5\) guards
• \(3\) forwards
• \(2\) centres Find the number of different selections if the lineup must include:
• At least \(1\) guard
• At most \(1\) forward
• Exactly \(1\) centre
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?
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)?
Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is a prime number?
Number of ways of distributing \(10\) identical chocolates among \(3\) children such that everyone gets at least one?
The number of bijective functions from set $A$ to itself when $A$ contains $97$ elements, is:
10 distinct points are taken on a circle. Then using these points
Statement I : The number of triangles that can be formed is 100
Statement II : The number of chords that can be formed is 45
Which of the following is correct?
How many ways can you arrange all the letters and numbers in "KCET 2025" which start with K and end with 5?
The number of 3-digit even numbers that can be formed with the digits 0, 1, 2, 3, 4, 5, 6 are
The sum of all 3-digit numbers that can be formed using $1,2,3,4$ without repetitions is
If ${}^9P_5 = (504)({}^6P_r)$, then the value of $r$ is equal to:
The number of arrangements containing all the seven letter of the word ALRIGHT that begins with LG is
Five digit number is formed using the digits 0, 1, 2, 3, 4, and 5 without repetitions. Number of five digit numbers which are divisible by 10 is:
A person travels from Hyderabad to Goa and returns, but does not use the same bus for both journeys. If there are 25 buses available for each direction, how many ways can the round trip be made?
The mean & variance of \(x_1, x_2, x_3, x_4\) is 1 and 13 respectively and the mean and variance of \(y_1, y_2, \dots, y_6\) be 2 and 1 respectively, the variance of \(x_1, x_2, \dots, x_4, y_1, y_2, \dots, y_6\) will be
A person has 3 different bags & 4 different books. The number of ways in which he can put these books in the bags so that no bag is empty, is
A person goes to college either by bus, scooter or car. The probability that he goes by bus is \(\frac{2}{5}\), by scooter is \(\frac{1}{5}\) and by car is \(\frac{3}{5}\). The probability that he entered late in college if he goes by bus is \(\frac{1}{7}\), by scooter is \(\frac{3}{7}\) and by car is \(\frac{1}{7}\). If it is given that he entered late in college, then the probability that he goes to college by car is
A bag contains $(N + 1)$ coins - $N$ fair coins, and one coin with 'Head' on both sides. A coin is selected at random and tossed. If the probability of getting 'Head' is $\frac{9}{16}$, then $N$ is equal to:
The number of 4-letter words, with or without meaning, each consisting of two vowels and two consonants that can be formed from the letters of the word INCONSEQUENTIAL, without repeating any letter, is:
Find number of ways of arranging 4 Boys \& 3 Girls such that all girls are not together :
The number of ways 4 boys and 3 girls are to be arranged in a row so that all 3 girls are not together, is equal to:
A regular polygon with \( n \) sides is given. \( P_n \) denotes number of triangles formed by joining any three points of given regular polygon. If \( P_{n+1} - P_n = 66 \), then the sum of all prime divisors of \( n \) is
If \( {}^{30}C_{30-r} + 3 \cdot {}^{30}C_{31-r} + 3 \cdot {}^{30}C_{32-r} + {}^{30}C_{33-r} = {}^{n}C_{r} \), then value of \( n \) is
Number of seven digits numbers which can be formed by using all the digits 1, 2, 3, 4, 5 with at least one digit repeated is _____.