Review for Combinatorics Exam #1

How many different bit strings are there of length 15?

• 15!

• 2¹⁵

• 15²

How many distinct ternary strings of length 16 exist?

(recall that a ternary string has alphabet {0,1,2})

• 16!

• 2¹⁶

• 3¹⁶

10 of 75 Bingo Balls have been pulled. How many ways are there to pull the next 5 balls,

one at a time?

• 75⋅74⋅73⋅72⋅71

• 65⋅64⋅63⋅62⋅61

50 students form a new club, In how many ways can they elect a President, a VP, and a Treasurer?

• 3⁵⁰

• 50⋅49⋅48

50 students form a club. In how many ways can they elect a president

and an advisory committee consisting of 3 people?

• 50⋅49⋅48⋅47

10 students show up to play basketball. In how many ways can they divide themselves

into 2 teams to scrimmage?

A ship has 8 flags of all different colors.

How many distinct signals are possible using all 8 flags?

• 2⁸

• 8!

• 7!

A ship has 8 flags of different colors.

How many different signals are possible using only 7 flags?

• 8!

• 7!

• 2⁷

A ship has 8 flags, 5 purple and 3 green.

How many different signals are possible using all 8 flags?

• 5!

• P(8,3)