=-.7truein =0truein =8truein =6truein truein truein truept

EXAM I

Let $U = \{1,2,3,4,5,6,7,8,9,10\}, A = \{1,3,5,7,9\}, B=\{2,4,6,8,10\}$ and $C =\{1,2,5,7,9\}$

1- Find $A \bigcap C$

2- Find $(A \bigcap C) \bigcup B$

3- Find $A \bigcap B$.

4- Let $A$ and $B$ be subsets of a set $S$ such that $n(A) =15, n(B)=24$ and $n(A \bigcap B) =12$ Find $n(A \bigcup B)$.

5- Let $A$ and $B$ be subsets of a set $S$ such that $n(A) =15, n(B)=24$. What is the largest possible value for $n(A \bigcup B)$? Is there a largest value for $n(S)$?

6- Evaluate $P(6,2)$.

7- How many groups of $4$ students can be chosen from a class of $15$ students? How many committees consisting of 1 president, 1 vice president and 2 members can be chosen from a class of $15$ students?

150 people in a sporting goods store filled out a questionnaire. These are the results:

• 70 people played tennis.
• 53 played golf
• 81 went swimming
• 50 played tennis and went swimming
• 23 went swimming and played golf
• 17 played tennis and golf
• 12 did all three

8- express the above data in a Venn diagram.

9- How many went swimming?

10- How many did not do any of these activities?

11 - Evaluate $C(10,6)$.

An Urn contains 18 numbered balls. 10 are white and 8 are red.

12- In how many ways can a sample of 6 balls be drawn from the Urn?

13- How many samples contain 3 red and 3 white balls?

14- How many samples contain at least one red ball?

15- An I.D. code consists of 3 numerals followed by 4 letters. How many code numbers ae there, if the letters are distinct, but the numbers can repeat themselves? (i.e. 112face) If the letters and numbers can repeat?