Ajay Kumar Solutions for Chapter: Numerical Ability, Exercise 16: Practice set

There are six boxes, numbered $1, 2, 3, 4, 5, and 6$. Each box is to be filled up either with a white ball or black ball in such a manner that at least one box contains a black ball and all the boxes containing black ball are consecutively numbered. In how many ways this can be done?

A letter lock consists of three rings each marked with $10$ different letters. In how many ways it is possible to make an unsuccessful attempt to open the lock?

A $51$ cm rod is built from $5$ cm rods and $2$ cm rods. All of the $5$ cm rod must comes first, and are followed by the $2$ cm rods. For example, the rod could be made from seven $5$ cm rods followed by eight $2$ cm rods. How many ways are there to build the $51$ cm rod?

In how many ways can the $18$ members of a boy count troop elect a president, a vice-president and a secretary, assuming that no member can hold more than one office?

A candidate is required to answer six out of ten questions which are divided into groups, each containing five questions, and he is not permitted to attempt more than $4$ from any group. In how many ways can he make up his choice?

How many arrangements of three types of flowers and if there are $6$ types to choose from?

Find the number of different arrangements of the letters of the word BANANA?

A farmer given $7$ full, $7$ half-full and $7$ empty bottles to his three sons and asks them to share these among themselves such that each of them gets the same amount of honey and the same number of bottles. In how many ways can this be done? (Bottles cannot be distinguished otherwise, they are sealed and cannot be broken).