Probability

Complements

Relative Complement

         

The student council of Ray School consists of 66 seniors, 55 juniors, and 33 sophomores. How many ways are there to form a delegation of 44 representatives for a school board meeting if the delegation must consist only of juniors and seniors and must include at least 11 junior?

Tina has chosen some books at the book store, and she would like to buy: 66 novels, 66 math books, and 33 biographies. However, Tina can only afford to buy 44 books.

Since she can't buy them all, if she needs at least 11 math book and puts back all the biographies, how many difference choices of books could she make?

Ralph chooses 44 numbers among 4,5,64, 5, 6 and 77, with duplication allowed, to create a 44-digit number larger than 60006000. How many ways can he obtain a number such that at least one of the middle two digits is 7?7?

In a town hall meeting, 100100 people voted on two issues aa and b.b. The results show that 5858 people voted in favor of aa and the rest voted against it, and 6868 people voted in favor of bb and the rest voted against it. Also, the number of people who voted against both aa and bb is greater by 44 than 13\frac{1}{3} of the number of people who voted in favor of both aa and b.b. How many people voted in favor of both aa and b?b?

Liza picks 44 distinct numbers from 1,2,3,4,51, 2, 3, 4, 5 to create a 44-digit number. How many ways are there to form a number such that either the first or last digit (or both) is even?

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