Curriculum · Counting & Probability · Permutations & Combinations

Permutations & Combinations

Arrangements, selections, and the bridge between them — with repeated elements handled honestly.

Objectives

Choose between nPr and nCr
Handle repeated objects
Count circular arrangements

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Permutations & Combinations mastery now.

Train the topic

●●○○○How many distinct arrangements does the word LEVEL have?AMC 8 style ●●○○○A club of

10

students chooses a committee of

3

. How many committees are possible?AMC 8 style ●●●○○Six people sit around a round table. Two of them insist on sitting together. How many seatings are there, if rotations are considered identical?AMC 10 style ●●●○○How many lattice paths go from

(0,0)

(4,4)

using only unit steps right and up?AMC 10 style