Out of 5 mathematicians and 7 physicists, a committee consisting of 2 mathematicians and 3 physicists is to be formed. In how many ways can this be done if two particular mathematicians cannot be on the committee? Your answer

You and 3 friends are moving into a 4-bedroom house and need to decide who gets which room. How many different ways could you and your friends assign the rooms? (Enter your answer as a whole number.)

There are 5 women and 8 men in a department.  How many ways can this committee be selected if there must be 2 men and 2 women on the committee?

The 2015 Ford Mustang Fastback is available in 5 models (V6, GT, etc.) with 10 choices of color, 2 choices of transmission, and 6 types of leather interior. How many different variations of this car does Ms. Thompson have to choose from when she is buying a car?

There are 5 men and 8 women auditioning to be in the school play. Answer the following questions: 1. If the cast consists of 2 women and 2 men, how many different casts can be selected? 2. If the cast consists of 2 women or 2 men, how many different casts can be selected?

In a group of 50 students, 25 are taking Math, 20 are taking Science, and 10 are taking both Math and Science. How many students are not taking either Math or Science?

There are 12 seniors and 8 juniors in the Mercy College Chess Club. In how many ways can a team consisting of 7 seniors and 3 juniors be selected from the Chess Club members?