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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Showing 4 comments:

Help

where does 3! and 2! come from?

10 months ago  Like

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.

10 months ago  Like

Math student

How did you get 3360

10 months ago  Like

Math student

dividing the factorials of 8!= 40,320 / 3!= 6 x 2!=2 so 40,320/12=3360
8!= 8x7x6x5x4x3x2x1= 40,320

10 months ago  Like

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