Answer to Question #94156 in Combinatorics | Number Theory for ACE

Question

AN OFFICE SECRETARY TRIES TO DEVICE CODING SCHEME FOR CERTAIN RECORDS, USING DIGITS 1 TO 4. SHE WANTS TO FIND THE TOTAL NUMBER OF CODES OF DIFFERENT DIGITS. IF ONLY THREE OF THE FOUR DIGITS ARE USED

Answer 1

We should choose three digits and order is important for us,

then we can count it as A(4,3)=((4!)/(1!))=24 by the formula of counting permutations without repetition.

Every choice represents some code. The answer is 24.