The letters of the word STAR are written on individual cards. If you always choose three cards and then put them back before the next set of three cards, how many different permutations will you have?

List all the different permutations in the space provided.

Question

The letters of the word STAR are written on individual cards. If you always choose three cards and then put them back before the next set of three cards, how many different permutations will you have?

List all the different permutations in the space provided.

kirbykirby · Answer

STA
SAT
TSA
AST
ATS
TAS

STR
SRT
TSR
RST
RTS
TRS

A methodological way of proceeding is to fix the first letter (Say "S") then permute the two other letters, then put S in the 2nd position, permute the 2 other letters, and then put S in the final position, and permute the 2 letters.

Do this as I did above with the letters STA, STR
what is remaining:
TAR
SAR

There should be 24 in total (Since $\small 4 \large P \small 3 \large= 24$)