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

In a conference $10$ speakers are present. If $S_1$ wants to speak before $S_2$ and $S_2$ wants to speak after $S_3,$ then the number of ways all the $10$ speakers can give their speeches with the above restriction if the remaining seven speakers have no objection to speak at any number is

If the different permutations of the word $\mathrm{EXAMINATION}$ are listed as in a dictionary, then how many words (with or without meaning) are there in this list before the first word starting with $M$.

The number of ways in which a mixed double game can be arranged amongst $9$ married couples, if no husband and wife play in the same game, is

How many divisors of $21600$ are divisible by $10$ but not by $15?$

Seven cards and seven envelopes are numbered $1, 2, 3, 4, 5, 6, 7$ and cards are to be placed in envelopes so that each envelope contains exactly one card and no card is placed in the envelope bearing the same number and moreover the card number $1$ is always placed in envelope number $2$ and $2$ is always placed in envelope numbered $3,$ then the number of ways it can be done is

The number of ways of choosing triplets $\left(x, y, z\right)$ such that $z\ge$ max $\left\{x, y\right\}$ and $x, y, z\in \left\{1, 2, 3\dots \dots , n\right\}$ is

The streets of a city are arranged like the lines of a chess board. There are $m$ streets running North to South & $\text{'}n\text{'}$ streets running East to West. The number of ways in which a man can travel from $NW$ to $SE$ corner going the shortest possible distance is:

Number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner is equal to