How many ways are there to seat `n` married couples `(ngeq3)` around a table such that men and women alternate and each women is not adjacent to her husband.

The total number of ways of selecting a team of 3 men and 4 women from 5 men and 6 women is

One Indian and four American men and their wives are to be seated randomly around a circular table. Then the conditional probability that the Indian man is seated adjacent to his wife given that each American man is seated adjacent to his wife is

In how many ways can 3 ladies and 3 gentlemen be seated around a round table so that any two and only two of the ladies sit together?

There are n married couples at a party. Each person shakes hand with every person other than her or his spouse. Find the total m of hand shakes.

A person wants to buy a car. There are two brands of car available in the market and each brand has 3 veriant models and each model comes in five different colours. In how many ways she can choose a car to buy?

The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by

The number of ways in which a couple can sit around a table with 6 guests if the couple takes consecutive seats is

In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, 3 in the front and 4 at the back? How many seating arrangements are possible if 3 girls sit together in a back row on adjacent seats?

In how many ways can a committee of 3 men and 2 women be selected out of 7 men and 5 women?