91影视

Given that, the total no. of letters\(\left( n \right)\)=10

total no. of letter s=\(\left( {{n_1}} \right)\)=3

total no. of letter t=\(\left( {{n_2}} \right)\)=3

total no. of letter i=\(\left( {{n_3}} \right)\)=2

total no. of letter a=\(\left( {{n_4}} \right)\)=1

total no. of letter c=\(\left( {{n_5}} \right)\)=1

The Multinomial coefficient is

\(\left( {\begin{array}{*{20}{c}}n\\{{n_1},{n_2},{n_3}}\end{array}} \right) = \frac{{n!}}{{{n_1}!{n_2}!{n_3}!}}\)

Here,

\(\begin{aligned}{}\left( {\begin{aligned}{*{20}{c}}{10}\\{3,3,2,1,1}\end{aligned}} \right) &= \frac{{10!}}{{3!3!2!1!1!}}\\ &= \frac{{3628800}}{{6 \times 6 \times 2 \times 1 \times 1}}\\ &= 50400\end{aligned}\)

Hence, if the given letters are arranged in random order, we can get 50400 possible ways.

The required probability is given by,

\(\begin{aligned}{c}p &= \frac{1}{{\left( {\begin{aligned}{*{20}{c}}{10}\\{3,3,2,1,1}\end{aligned}} \right)}}\\ &= \frac{1}{{50400}}\end{aligned}\)

Therefore, the probability that given letters can be spelt as 鈥渟tatistics鈥� is \(\frac{1}{{50400}}\).