How do you find the number of distinct arrangements of the letters in STREETS?

Question

Brendon Fernandez · Accepted Answer

Step 1First, we can ask ourselves &quot;How many arrangements can we make with 7 things (letters in this case)&quot;The answer is 7! (We can choose 7 in the first slot, 6 in the next, etc)However, we must also take into account the repetition of some letters in the word STREETS.We can do this by dividing the repetition.The repetition occurs because we counted S in place of another S as a possible combination. However, this is not distinct.What is wrong: &quot;      S    T    R          E      1              E      2        T    S  &quot; is one combination and so is       S    T    R          E      2              E      1        T    S  .What is right:       S    T    R          E      1              E      2        T    S   and       S    T    R          E      2              E      1        T    S   are not distinct, so we only count them once.We divide the possible arrangements for EACH repeating letter.Step 2Since there are 3 repeating letters: S twice, T twice, E twice, we have                     7        !                    2        !        2        !        2        !            .Divide it all out and we have 630 distinct combinationsNote: for these types of problems, we can simply do total letters! / number of repeats of letter1 ! number of repeats of letter2 ! ... and so on for all repeating letters

How do you find the number of distinct arrangements of

Answered question

Answer & Explanation

New Questions in High school probability