Combinatorics

Question 1

number of arrangements of n distinct objects

Answer 1

n! (nPn)

eg number of ways to arrange the letters in a word

Question 2

number of arrangements of n objects taken r at a time without repetition

Answer 2

nPr

eg number of arrangements of 3 people getting 1st, 2nd, and 3rd in a race of 50 people

Question 3

number of arrangements of n objects taken r at a time with repetition

Answer 3

n^r

eg number of passwords with a 6 digit code

Question 4

number of arrangements of n objects, where there are n₁ of the 1st kind, and n₂ of the 2nd kind, and nk of the kth kind

Answer 4

n!/(n₁!n₂!…nk!)

Each factorial accounts for the num. of ways that the repeated can swap

eg number of arrangements of a word with repeated letters

Question 5

number of ways to select r objects from n distinct objects

Answer 5

nCr

eg number of ways 30 people can give everyone else a handshake

Question 6

n! (nPn)

Answer 6

number of arrangements of n distinct objects

Question 7

nPr

Answer 7

number of arrangements of n objects taken r at a time without repetition

Question 8

n^r

Answer 8

number of arrangements of n objects taken r at a time with repetition

Question 9

n!/(n₁!n₂!…nk!)

Answer 9

number of arrangements of n objects, where there are n₁ of the 1st kind, and n₂ of the 2nd kind, and nk of the kth kind

Question 10

nCr

Answer 10

number of ways to select r objects from n distinct objects