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