There are 5 men and 7 women auditioning to be in the school play. Answer the following questions

Question

If the cast consists of 2 women and 2 men, how many different casts can be selected?

If the cast consists of 2 women or 2 men, how many different casts can be selected?

Answer 1

The ways of choosing two women from 7 is 7 choose 2 or 21. The ways of choosing 2 men from five men is 5 choose 2 or 10. For the first part we want any combination of men and women, which could be seen with a two way table (the 21 combinations for women is the rows and the 10 combinations of men as the columns) This gives a total of 210 combinations. (Easy way to remember this is “and” means multiply. Similarly “or” means add.) Therefore the number of ways to choose 2 men or 2 women is 10 + 21 = 31