MTH 152: Final Examination Please show all necessary work. If not shown, partial

Question

MTH 152: Final Examination Please show all necessary work. If not shown, partial credits may be given at my discretion. Please put your LAST NAME on this page and attach this page in front of your answer sheets C.(Alan, Bill, Cathy, David, and evern). Consider a club c with nve members: Assuming all members are elgible, but that ne one can hold more than one office, show partial list with on president and count the different ways the club could elect a group of officers as follows: and a treasurer, if the president must be a man 2. 1· A president,a secretary, (30 points) Find the number of distinguishable arrangements of the letters of the following words: (a) Eight fair coins are tossed, find the number of ways to obtain more than six heads: Two fair coins are tossed (for example a nickel and a quarter). Give each of the following (30 points) (5 points MANASSAS (b) VIRGINIA 3. (10 points) 4. (a) The sample space (b) The probability of heads on the nickel. (c) The probability of heads on the quarter. (d) The probability of getting both heads. (e) The probability of getting the same outcome on both coins Kathy wants to have exactly two daughters. Assuming that boy and girl babies are equally likely, find her probability of success if she were to have four children altogether. 5. (10 points)

Explanation / Answer

2)
a) MANASSAS
1 - M, 3 - A, 1 - N, 3 - S
Total 8 letters.
8 letters can be arranged in 8! ways but in order to have distinguishable arrangements

8!/(3!*3!) = 1120

b) VIRGINIA
Total 8 letters,
3 - I

8 letters can be arranged in 8! ways but in order to have distinguishable arrangements

8!/(3!) = 6720

3.
We want to know how many ways we can have 7 or 8 heads
For 7 heads, 1 tail can be arranged in 8 ways along with 7 heads.
8 heads are possible only in one way

Hence total possible ways are 8+1 = 9

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