Arun Sharma Solutions for Exercise 2: Level of Difficulty

From $4$ gentlemen and $4$ ladies, a committee of $5$ is to be formed. Find the number of ways of doing so if the committee consists of a president, a vice president, and three secretaries?

From $4$ gentlemen and $4$ ladies, a committee of $5$ is to be formed. The committee consists of a president, a vice-president and three secretaries. What will be the number of ways of selecting the committee with at least $3$ women, such that at least one woman holds the post of either a president or a vice-president?

There are four envelopes and four letters. Find the number of ways in which only two letters goes in the wrong envelopes?

There are seven pairs of black shoes and five pairs of white shoes. They are all put in a box and shoes are drawn one at a time. What is the minimum number of shoes required to be drawn out to get at least one correct pair(Black or White shoes) of shoes?

In the Sunita Building in Mumbai, there are $12$ floors plus the ground floor. $9$ people get into the lift of the building on the ground floor. The lift does not stop on the first floor. If $2, 3$ and $4$ people alight from the lift on its upward journey, then in how many ways can they do so? (Assume they alight on different floors.)

There are $40$ doctors in the surgical department of the AIIMS. In how many ways can they be arranged to form a team with $1$ surgeon and $4$ assistant.

How many five-digit numbers, which do not contain identical digits, can be written by means of the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$?

How many different four-digit numbers can be written using $1, 2, 3, 4, 5, 6, 7, 8$ only once such that the number  $2$ is contained once?