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.

Correct answer:

p =  0.0298 %

Step-by-step explanation:

$$\begin{gathered} n_1=1 \\ n=8 \\ n(S)=3 \\ n(T)=1 \\ n(R)=1 \\ n(E)=2 \\ n(D)=1 \\ {n}_2=\frac{n!}{n(S)!\cdot n(T)!\cdot n(R)!\cdot n(E)!\cdot n(D)!} \\ {n}_2=\frac{8!}{3!\cdot 2!}=3360 \\ p=100\cdot \frac{n_1}{n_2}=100\cdot \frac{1}{3360}=\frac{100\cdot 1}{3360}=\frac{100}{3360}=0.0298\% \end{gathered}$$

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