Permutations and Combinations · Mathematics · WB JEE

Out of 8 given points, 3 are collinear. How many different straight lines can be drawn by joining any two points from those 8 points?

How many odd numbers of six significant digits can be formed with the digits 0, 1, 2, 5, 6, 7 when no digit is repeated?

The number of ways four boys can be seated around a round table in four chairs of different colours is

A polygon has 44 diagonals. The number of the sides is

The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

If $${}^{n - 1}{C_3} + {}^{n - 1}{C_4} > {}^n{C_3}$$, then n is just greater than integer

If $${}^n{C_4}$$, $${}^n{C_5}$$ and $${}^n{C_6}$$ are in A.P., then n is

The number of diagonals in a polygon is 20. The number of sides of the polygon is

$${}^{15}{C_3} + {}^{15}{C_5} + \,\,......\,\, + {}^{15}{C_{15}} = $$

If ${ }^9 P_5+5 \cdot{ }^9 P_4={ }^{10} P_r$, then the value of '$r$' is

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

The numbers $$1,2,3, \ldots \ldots, \mathrm{m}$$ are arranged in random order. The number of ways this can be done, so that the numbers $$1,2, \ldots \ldots ., \mathrm{r}(\mathrm{r}<\mathrm{m})$$ appears as neighbours is

Five balls of different colours are to be placed in three boxes of different sizes. The number of ways in which we can place the balls in the boxes so that no box remains empty is

$$ \text { If } 1000!=3^n \times m \text { where } m \text { is an integer not divisible by } 3 \text {, then } n= $$

The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels is

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one of them will not get any object is

Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the elements of P. A subset Q of A is chosen again. The number of ways of choosing P and Q such that Q contains just one element more than P is

There are n white and n black balls marked 1, 2, 3, ...... n. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is

How many triangles can be formed by joining 6 points lying on a circle?

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then