Counting Techniques

My initials are CSP since I have a first name, middle name, and last name. How many different sets of three initials are possible?

• 78

• 17,576

• 15,600

• 27

How many ways can 9 books be arranged in a row on a shelf?

• 9

• 45

• 181,440

• 362,880

A password must be two digits followed by three letters. If repeats of symbols ARE allowed, how many passwords are possible?

• 10 X 9 X 26 X 25 X 24

• 10 X 10 X 26 X 26 X 26

• 10 + 10 + 26 + 26 + 26

• 10 + 9 + 26 + 25 + 24

How many ways can 6 paintings be arranged in a row on a wall?

• 720

• 6

• 21

• 36

What is "!" called in counting methods?

• exclamation point

• factorial

• Multiply a lot

In how many ways can you arrange the letters of the word EDUCATION such that the vowels are always together?

• 120 ways

• 14400 ways

• 362880 ways

• 6547234 ways

A code is to be formed using A, B, C , D, E, F, 5, 6, 7, or 8. If the code must consist of 4 letters followed by 3-digit numbers, how many codes can be formed without repetition?

• 144

• 8640

• 604800

• 3628800

Jericho has 6 durians, 5 papayas, and 2 apples. If he wants to arrange these fruits of the same kind have to be grouped together, calculate the numbers of different arrangements. The sizes of the fruits are different.

• 1036800

• 691200

• 518400

• 172800

A certain restaurant allows you to assemble your own vegetable salad. If there are 8 kinds of vegetables available, how many variations of the salad can you make containing at least 5 vegetables?

• 56

• 84

• 93

• 96

There are six people people, including you and your enemy, in a line. In how many ways can you arrange yourselves such that you and your enemy will never be beside each other?

• 240 ways

• 720 ways

• 480 ways

• 670 ways