×
Back to all chapters

# Complements

You are in the complement of the set of people who are not Brilliant.

# Relative Complement

The student council of Ray School consists of $$6$$ seniors, $$5$$ juniors, and $$3$$ sophomores. How many ways are there to form a delegation of $$4$$ representatives for a school board meeting if the delegation must consist only of juniors and seniors and must include at least $$1$$ junior?

Tina has chosen some books at the book store, and she would like to buy: $$6$$ novels, $$6$$ math books, and $$3$$ biographies. However, Tina can only afford to buy $$4$$ books.

Since she can't buy them all, if she needs at least $$1$$ math book and puts back all the biographies, how many difference choices of books could she make?

Ralph chooses $$4$$ numbers among $$4, 5, 6$$ and $$7$$, with duplication allowed, to create a $$4$$-digit number larger than $$6000$$. How many ways can he obtain a number such that at least one of the middle two digits is $$7?$$

In a town hall meeting, $$100$$ people voted on two issues $$a$$ and $$b.$$ The results show that $$58$$ people voted in favor of $$a$$ and the rest voted against it, and $$68$$ people voted in favor of $$b$$ and the rest voted against it. Also, the number of people who voted against both $$a$$ and $$b$$ is greater by $$4$$ than $$\frac{1}{3}$$ of the number of people who voted in favor of both $$a$$ and $$b.$$ How many people voted in favor of both $$a$$ and $$b?$$

Liza picks $$4$$ distinct numbers from $$1, 2, 3, 4, 5$$ to create a $$4$$-digit number. How many ways are there to form a number such that either the first or last digit (or both) is even?

×