# 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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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:

Need help calculate sum, simplify or multiply fractions? Try our fraction calculator. Our percentage calculator will help you quickly calculate various typical tasks with percentages. See also our combinations with repetition calculator. Would you like to compute count of combinations? See also our permutations calculator. See also our variations calculator.

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