Using arrangements of words, it is found that the statement is true.
------------------
- Suppose a word has n letters.
- Considering that m of these letters are repeating, each [tex]n_1,n_2,...,n_m[/tex] times.
- The number of distinct ways the word can be arranged is given by:
[tex]N = \frac{n!}{n_1\times n_2 \times ... n_m}[/tex]
------------------
- The word "sleeplessness" has 13 letters.
- s repeats 5 times.
- e repeats 4 times.
- l repeats 2 times.
Thus, the number of ways to arrange the letters is given by:
[tex]N_1 = \frac{13!}{5!4!2!}[/tex]
------------------
- The word "senselessness" has 13 letters.
- s repeats 6 times.
- e repeats 4 times.
- n repeats 2 times.
Thus, the number of ways to arrange the letters is given by:
[tex]N_2 = \frac{13!}{6!4!2!}[/tex]
------------------
Finding the ratio of [tex]N_2[/tex] to [tex]N_1[/tex]:
[tex]\frac{N_2}{N_1} = \frac{\frac{13!}{5!4!2!}}{\frac{13!}{6!4!2!}} = \frac{13!}{5!4!2!} \times \frac{6!4!2!}{13!} = \frac{6!}{5!} = 6[/tex]
Thus, since the ratio is 6, the statement is true.
A similar problem is given at https://brainly.com/question/16790460
