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.


p =  0.03 %


n1=1 n2=8!3! 2!=3360  p=100 n1n2=100 13360=51680.0298=0.03%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 \%



Showing 4 comments:
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


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