Problem 1

A card is randomly picked from a deck of 52 cards. What is the probability that the card is a

a.A spade?

b.A king or queen?

c.A heartandking?

d.A king and queen?

Problem 2

In a group of 6 boys and 4 girls, five children are to be selected to participate in an event.

a.In how many different ways can the five children be selected?

b.In how many different ways such that there is at least one boy?

c.In how many different ways such that there are at least two boys and one girl?

Problem 3

A delegation of 4 employees is selected each year from a department to attend the National Convention of Innovators' annual meeting.

a.In how many ways can the delegation be chosen if there are 12 eligible employees?

b.In how many ways if two of the eligible employees will not attend the meeting together?

c.In how many ways if two eligible employees are married and will only attend the meeting together?

Problem 4

How many different signals, each consisting of 8 flags hung in a vertical line can be formed from a set of 4 red flags, 3 white flags and a blue flag?

a.If all flags of the same color are distinguishable?

b.If all flags of the same color are identical?

Problem 5

How many 3-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS',

a.If repetition of letters is allowed?

b.If repetition of letters is not allowed?

Problem 6

a.In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?

b.In how many different ways can the letters of the word 'CORPORATION' be arranged so that the vowels always come together?

Problem 7

Five high-profile guests, A, B, C, D and E, are invited to a corporate dinner party.

a.In how many ways can these 5 people be seated at a round table?

b.In how many ways so that A and B must always sit together.

c.In how many ways so that C and D must not sit together.