Need the following assignment At a certain university 523 of

Need the following assignment:

At a certain university 523 of the seniors are history majors or math majors (or both). There are 100 senior math majors, and 33 seniors are majoring in both history and math. How many seniors are majoring in history? How many 4-digit positive integers are there that are even or contain no 0\'s? Is the following statement true or false? Explain. If A_1 intersection A_2 intersection A_3 = phi, then| A_1 union A_2 union A_3| = | A_1| + | A_2| + | A_3|. 7. This problem concerns 4-card hands dealt off of a standard 52-card deck. How many 4-card hands are there for which all 4 cards are of the same suit or all 4 cards are red?

Solution

1. It uses union theorem that

(AB)=(A)+(B)(AB)

Here A union B is 523, A is 100 and A intersection B is 33 so equation becomes

523=100+B-33

B=523+33-100

B=456

So 456 are majoring in History