A test contains three parts: Part A, Part B and Part C. Part A contains 4, Part B contains 6 and Part C contains 5 questions respectively. A student must answer 10 questions.
a. How many selections are possible if a student must select two questions from Part A?
b. How many selections are possible if a student must answer at least 4 questions from each part?
A company has 1150 employees. Each employee is to be given an ID number that consists of two letters (must be vowels) followed by three digits (even digits only). Is it possible to give each employee a different ID number using this scheme? Explain.
In how many ways can 8 students of a class can be arranged in a row, if:
a. No restrictions are applied.
b. Anny and Sarah as well as Jane and Jill want to stand together.
c. Only Anny, Sarah and Miranda want to stand next to each other.
There are Y balls in a bag. Of them 5 are pink and 2 are orange. Rest of the balls are green and white. Paul selects any two balls randomly with replacement. The probability that he selects a Pink and then an Orange ball is 1/10. Find out the total number of balls in the bag. Can you find the probability of selecting a Green ball from the bag? Explain.

Suppose that the height of the UCLA female students has normal distribution with mean 62 inches and variance 64 inches
a. Find the Interquartile range of the heights of UCLA female students.
b. What is the range of the middle 99% heights of UCLA female students?
c. What percentage of UCLA female students are more than 78 inches and less than 46 inches?
Three biased coins were flipped and the number of heads were recorded. From past data the following probabilities were found:
Coin 01: P (H) = 0.70
Coin 02: P (H) = 0.30
Coin 03: P (T) = 0.60
a. Find the probability distribution of the number of heads recorded.
b. Draw a Histogram of the result.
c. Comment on the shape of the distribution.

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