Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 1: Exercise 1

If the maximum number of trials required to open all locks when there are $n$ locks and $n$ keys is $105$, then $n$ equals

Let $P_m$ stand for ${}^{m}P_{m\text{'}}$ then, $1+P_1+2P_2+3P_3+.......+n{P}_n$ is equal to

The total number of ways in which four boys and four girls can be seated around a round table, so that no two girls sit together is equal to

In a badminton tournament each player played one game with all the other players. Number of players participated in the tournament if they played $105$ games is

The number of rectangles, of any size excluding squares from the rectangle of size $8\times 7$ is

The number of ways in which a pack of $52$ cards can be divided equality into four groups, is

The number of non-negative integral solutions of $x+y+z\le n$, where $n\in N$ is

The number of ways in which an examiner can assign $30$ marks to $8$ questions, giving not less than $2$ marks to any question, is