IPMAT Permutation and Combination Questions 2026 PDF

Please calculate in how many ways can a platoon of sixteen soldiers be chosen out of a total of twenty soldiers for a surgical strike?

There are 12 copies of Beetles CDs, 7 copies of Pink Floyd CDs, 3 different CDs of Michael Jackson, and 2 different CDs of Madonna. Find the number of ways in which one or more than one CD can be selected?

Eight teams participate in a tournament where each team plays against every other team exactly once. In a particular year, one team got suspended after playing 3 matches, due to a disciplinary issue. The organisers decided to proceed, nonetheless, with the remaining matches. The total number of matches that were played in the tournament that year is

A box contains 2 white shirts, 3 black shirts, and 4 red shirts. In how many ways can 3 shirts be drawn from the box, if at least one black shirt is to be included in the draw?

Five racquets needs to be placed in three boxes. Each box can hold all the five racquets. In how many ways can the racquets be placed in the boxes so that no box can be empty if all racquets are different but all boxes are identical?

Please calculate in how many ways can a set of five players be formed out of a total of ten players such that two particular players should be involved in each set?

In how many ways can the letters of the word MANAGEMENT be arranged such that no two vowels appear together?

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays
• against every other player belonging to one's own group exactly once;
• against each player belonging to one of the remaining three groups exactly twice;
• against each player belonging to one of the remaining two groups exactly three times; and
• against each player belonging to the remaining group exactly four times.
If there are more than 1000 matches being played in the tournament, the minimum possible number of players in each group is_______.

The number of integers greater than 5000 and divisible by 5 that can be formed with the digits 1, 3, 5, 7, 8, 9 where no digit is repeated is

In a chess tournament there are 5 contestants. Each player plays against all the others exactly once. No game results in a draw. The winner in a game gets one point and the loser gets zero point. Which of the following sequences cannot represent the scores of the five players?

How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?

Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is _____________.

Mrs and Mr Sharma, and Mrs and Mr Ahuja along with four other persons are to be seated at a round table for dinner. If Mrs and Mr Sharma are to be seated next to each other, and Mrs and Mr Ahuja are not to be seated next to each other, then the total number of seating arrangements is _________.

The number of 5-digit numbers consisting of distinct digits that can be formed such that only odd digits occur at odd places is

A rabbit is sitting at the base of a staircase which has 10 steps. It proceeds to the top of the staircase by climbing either one step at a time or two steps at a time. The number of ways it can reach the top is

The number of four-digit integers which are greater than 1000 and divisible by both 2 and 3, but not by 5, is

Consider an 8 $$\times$$ 8 chessboard. The number of ways 8 rooks can be placed on the board such that no two rooks are in the same row and no two are in the same column is

The number of values of x for which $$C\left(\begin{array}{c}17-x\\ 3x + 1\end{array}\right)$$ is defined as an integer is

Can you calculate in how many ways can 7 tennis players can be seated in a circular order?

Let $$n$$ be the number of ways in which $$20$$ identical balloons can be distributed among $$5$$ girls and $$3$$ boys such that everyone gets at least one balloon and no girl gets fewer balloons than a boy does. Then