Questions:
1. A certain organization recommends the use of passwords with the following format: vowel, consonant, vowel, number (for example, oba3).
a) Assume that repeats are allowed:
i) Assume passwords are not case sensitive, how many such passwords are possible?
ii) How many passwords are possible if they are case sensitive?
b) Assume that repeats are not allowed:
i) Assume passwords are not case sensitive, how many such passwords are possible?
ii) How many passwords are possible if they are case-sensitive?
2. From a group of 8 women & 12 men, a committee consisting of 4 different people is to be formed.
a) How many different committee are possible?
b) How many different ways to form a committee with a chairperson, first vice chairperson, second vice chairperson and secretary?
c) Find the probability of having exactly 2 men on the committee.
d) Find the probability of having at least 1 woman on the committee.
3. Suppose a compact disk (CD) you just purchased has 15 tracks. After listening to the CD, you decide that you like 6 of the songs. The shuffle feature on your CD player will play each of the 15 songs once in a random order. Find the probability that among the first 5 songs played
a) you like 1 of them
b) you like none of them
c) you like at least 2 of them