Counting Techniques Mixed Review

How many different ways can 8 people be arranged in a row to take a picture?

The password for an account must be two letters followed by two digits. Repetitions of letters or digits ARE allowed. How many different passwords are possible?

The password for an account must be two letters followed by two digits. Repetitions of letters or digits are NOT allowed. How many different passwords are possible?

There are 15 students in a class. How many different ways could two students be selected to carry a box to the office?

There are 16 students in a club. How many different ways could the elect a president and vice-president?

How many different ways can you rearrange the letters in the word FATHER?

How many different ways can you rearrange the letters in the word SISTER?

Antonio has four shirts, three pairs of pants, and four hats. How many different outfits can he make?

A passcode must be two digits followed by three letters. How many passcodes are possible if repetitions are NOT allowed?

• $10\times10\times26\times26\times26$

• $10\times9\times26\times25\times24$

• $10!$

• $10\times9\times8\times7\times6$

How many ways can a president, vice-president, and secretary be selected from a club that has 42 members?

• $42!$

• $42\times3$

• 42 nPr 3

• 42 nCr 3