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,

$N=\frac{n!}{r_1!r_2!\ldots r_k!}$

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

$N=\frac{n!}{r_1!r_2!r_3!}$

Substituting the values,

$\begin{gathered} N=\frac{12!}{4!3!2!} \\ =\frac{12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{(4\times3\times2\times1)\times(3\times2\times1)\times(2\times1)} \\ =1663200 \end{gathered}$

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