IPMAT Indore: Modern MathPermutation & Combination. Free, no login required.

The number of ways in which coins of denominations of rupees 2, 5 and, 10 can be combined to make a value of rupees 50 is

The number of ways in which three distinct integers can be chosen from the set $\{1, 2, \ldots, 9\}$ such that their product is divisible by 4, 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

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

If 5 boys and 3 girls sit randomly around a circular table, the probability that there will be at least one boy sitting between any two girls is

The number of solutions of the equation $x_1 + x_2 + x_3 + x_4 = 50$, where $x_1, x_2, x_3, x_4$ are integers with $x_1 \geq 1, x_2 \geq 2, x_3 \geq 0, x_4 \geq 0$ is

The number of values of $x$ for which $C \binom {17-x}{3x+1}$ is defined as an integer is

In a chess tournament, there are four groups, each containing an equal number of players. Each player plays

1. against every other player belonging to one's own group exactly once;
2. against each player belonging to one of the remaining three groups exactly twice;
3. against each player belonging to one of the remaining two groups exactly three times; and
4. 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 total number of positive integer solutions of $21 ≤ a + b + c ≤ 25$ 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

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 triangles that can be formed by choosing points from 7 points on a line and 5 points on another parallel line is _________.

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

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 _________.

There are 5 parallel lines on the plane. On the same plane, there are $n$ other lines that are perpendicular to the 5 parallel lines. If the number of distinct rectangles formed by these lines is 360, what is the value of $n$?

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

There are 10 points in the plane, of which 5 points are collinear and no three among the remaining are collinear. Then the number of distinct straight lines that can be formed out of these 10 points is

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

How many different numbers can be formed by using only the digits 1 and 3 which are smaller than 3000000?