How many ways can five people A , B , C , D and E sit in a row at a movie theatre if D and E will not sit next to each other ?

A class contains eight boys and eight girls. In how many ways can they stand in a line if they must alternate in gender (no two boys and no two girls are standing next to one another)?

suppose that we wish to seat 10 people, 5 men and 5 women, in a row of ten chairs. in how many ways can we seat the people if all men sit together and all women sit together

In how many ways can 4 CS students and 5 IT students sit in a row if the CS and IT students must alternate?

Delegates from 10 countries, including Russia, France, England, and the United States, are to be seated in a row. How many different seating arrangements are possible if the French and English delegates are to be seated next to each other, and the Russian and U.S. delegates are not to be next to each other?

Suppose you have a choice of ten TV sets that can be matched with any of six DVR players and eight DVD players. How many different TV/DVR/DVD systems can you assemble?

Suppose that a department contains 10 men and 15 women. How many ways are there to form a committee with six members if it must have more women than men?

In how many ways can a subcommittee of eight be chosen from a Senate committee of seven Democrats and six Republicans if The subcommittee must consist of four Republicans and four Democrats?

You have 4 indistinguishable gold coins and 4 indistinguishable silver coins. Each coin has a side that is heads and a side that is tails. You want to stack the eight coins on a table into a single stack so that no two adjacent coins are face to face. Find the number of possible distinguishable stacks of the 8 coins.

In how many ways can 6 boys and 7 girls sit in a row if the girls and boys must alternate?