Work Book Exercise 6.1

An examination paper contains $8$ questions of which $4$ have $3$ possible answers, $3$ have $2$ possible answers and the remaining one question has $5$ possible answers. The total number of possible answers to all the questions is

There are stalls for $10$ animals in a ship. The number of ways in which ship load can be made, if there are cows, calves and horses to be transported, animals of each kind being not less than $10$ is

A letter lock consists of three rings, each marked with $10$ different letters. The number of ways in which it is possible to make an unsuccessful attempt to open the lock is

How many two-digit even numbers can be formed from the digits $1,2,3,4,5,$ if the digits can be repeated?

A five-digit number divisible by $3$ is to be formed by using the digits $0, 1, 2, 3, 4$ and $5$ without repetition. The total number of ways in which this can be done is

If $p, q\in \left\{1, 2, 3, 4\right\}$, then the number of equations of the form $p{x}^2+qx+1=0$ having real roots, is

Find the number of ordered pairs $\left(x,y\right),$ if $x, y \in \{0,1,2,3,\dots ,10\}$ and if $\left|x-y\right|>5$

Find the total number of ways in which two small squares can be selected on the normal chessboard, if they are not in same row or same column.