[tex] \large \bold{PROBLEM:}[/tex]
STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
[tex] \large{ \bold{SOLUTION:}} \\ \large\begin{aligned}{\bold{n_1=1}}\\\bold{n=8}\\\bold{n(S)=3}\\\bold{n(T)=1}\\\bold{n(R)=1}\\\bold{n(E)=2}\\\bold{n(D)=1}\end{aligned}[/tex]
[tex]\large\begin{aligned}{\bold{n_2=\frac{n!}{n(S)!·n(T)!·n(R)!·n(E)!·n(D)}}} \\ \\ \large \bold{n_2} = \frac{8!}{3!·2!} \\ \large \bold{P = 100· \frac{n_1}{n_2} = 100 ·\frac{1}{3360} = \frac{5}{168} = 0.0298\%} \\ \\ \bold{ ANSWER:}\large \dashrightarrow \boxed{ \bold{0.0298\%}}\end{aligned}[/tex]
