Embibe Experts Solutions for Chapter: Permutation and Combination, Exercise 3: Exercise-3

The total number of ways in which $5$ balls of different colours can be distributed among $3$ persons so that each person gets at least one ball, is

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that exactly $4$ girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

A debate club consists of $6$ giris and $4$ boys. A team of $4$ members is to be selected from this club including the selection of a captain (from among these $4$ members) for the team. If the team has to include at most one boy. Then the number of ways of selecting the team is

Words of length $10$ are formed using the letters $A, B, C, D, E, F, G, H, I, J.$ Let $x$ be the number of such words where no letter is repeated; and let $y$ be the number of such words where exactly one letter is repeated twice and no other letter is repeated, then $\frac{y}{9x}=$

From $6$ different novels and $3$ different dictionaries, $4$ novels and $1$ dictionary are to be selected and arranged in a row on the shelf so that the dictionary is always in the middle. Then the number of such arrangements is

There are $10$ points in a plane, out of these $6$ are collinear. If $N$ is the number of triangles formed by joining these points, then

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from $10$ white, $9$ green and $7$ black balls is

If all the words (with or without meaning) having five letters, formed using the letters of the word $\mathrm{SMALL}$ and arranged as in a dictionary; then the position of the word $\mathrm{SMALL}$ is