Permutation and combination practice · Medium

The number of permutations of 4 letters from the letters of word 'KOLKATA' is

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is:

The value of $\frac{{ }^{20} C_n}{{ }^{25} C_m}$ when both numerator and denominator have their greatest values, is

A class has 21 students. The class teacher has been asked to make $n$ groups of $r$ students each and go to zoo taking one group at a time. The size of group zoo i.e. the value of $r$) for which the teacher goes to the maximum number of times is (no group can go to the zoo twice)

The number of 3 digit numbers ' $a b c$ ' such that $b < c$ is

Five balls of different colours are to be placed in three boxes of different sizes. Each box can hold all five balls. In how many ways can we place the balls so that no box remains empty?

The number of arrangements that can be formed from the letters $a, b, c, d, e, f$ taken 3 at a time without repetition and each arrangement containing at least one vowel, is

Let $A = \left\{ {{x_1},{x_{2,}}{x_3},\;{x_4},\;{x_5},\;{x_6}} \right\}$,
$B = \left\{ {{y_1},\;{y_2},\;{y_3},{y_4},{y_5},{y_6}} \right\}.$ . Then the number of one – one mapping from $A$ to $B$ such that $f\left( {{x_i}} \right) \ne {y_v}i = 1,\;2,\;3,\;4,\;5,\;6$

In a country, no two persons have identical set of teeth and there is no person without a tooth, also no person has more than 32 teeth. If shape and size of tooth is disregarded and only the position of tooth is considered, then maximum population of that country can be

The number of ways in which the letters of 'ARRANGE' be arranged so that i. "No two R's come together is