# 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.

Result

p =  0.03 %

#### Solution:

$n_{ 1 } = 1 \ \\ n_{ 2 } = \dfrac{ 8! }{ 3! \cdot \ 2! } = 3360 \ \\ \ \\ p = 100 \cdot \ \dfrac{ n_{ 1 } }{ n_{ 2 } } = 100 \cdot \ \dfrac{ 1 }{ 3360 } = \dfrac{ 5 }{ 168 } \doteq 0.0298 = 0.03 \%$

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...): Help
where does 3! and 2! come from? Dr Math
some characters are repeated: 3xS + 2xE; so there is no difference between first second and third S or 1st or 2nd E char. Math student
How did you get 3360 Math student
dividing the factorials of 8!= 40,320 / 3!= 6 x 2!=2 so 40,320/12=3360
8!= 8x7x6x5x4x3x2x1= 40,320 #### Following knowledge from mathematics are needed to solve this word math problem:

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