Sarvesh K Verma Solutions for Chapter: Permutations & Combinations, Exercise 4: Introductory Exercise

$9$ persons were invited for a business meeting by Ambani, where the host be seated at a circular table. How many different arrangements are possible if two invitees viz., Sahara and Mahindra be seated on either side of the host Ambani?

There are $3$boys and $4$girls, seated around a circular table so that no two boys are together. Find the number of ways in which this can be done.

$7$sisters dine at a round table. They dine together till each of them dine with different neighbours i.e., they do not like to dine with same neighbours in any

Find the number of ways in which $10$different flowers can be strung to form a garland so that $3$particular flowers are always together.

$3$male and $3$female singers sat around a circular table. Alka is a female singer did not sat adjacent to a male singer and Sonu is a male singer did not sat adjacent to a female singer. In how many ways this could be done?

Three couples book a table for six people at a restaurant that has only circular tables. If no husband sits opposite his wife, in how many ways can three couples be arranged to sit around the table?

Twelve students are called for the group discussion of which no two students have the same rank. They sit in a circle for the group discussion in such a way that the students sitting just next to either side of any student should have either higher rank or lower rank. Find the number of ways in which they can be arranged.

In a single-occupancy co-ed hostel, consisting of $20$rooms, exactly $10$guys and $10$girls are allowed to stay in. Each one of them stays in a separate room. The hostel is designed in a circular form such that the door of a room opens opposite the door of another room. In how many ways can the rooms be allocated to them so that whenever a guy looks either side of his door there is always a girl next door?