Question

How many different ways are there to arrange the letters in the phrase "stats is sweet"?

Answer 1

The phrase "stats is sweet" has n=12 letters.

The letters s, t and e are repeated in the phrase.

The number of "s" in the phrase, r1=4.

The number of "t" in the phrase, r2=3.

The number of "e" in the phrase, r3=2.

Using permutation, if there are n objects with r1 objects of one type, r2 letters of another type ....and rm letters of another kind, then the number of ways of arrangement is,

`N=(n!)/(r_1!r_2!\ldots r_k!)`

Hence, the number of ways the letters in the phrase "stats is sweet" can be arranged is,

`N=(n!)/(r_1!r_2!r_3!)`

Substituting the values,

`\begin{gathered} N=(12!)/(4!3!2!) \\ =(12*11*10*9*8*7*6*5*4*3*2*1)/((4*3*2*1)*(3*2*1)*(2*1)) \\ =1663200 \end{gathered}`

Therefore, the number of ways the letters in the phrase "stats is sweet" can be arranged is 1663200.