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.

Correct result:

p =  0.0298 %


n1=1 n=8 n(S)=3 n(T)=1 n(R)=1 n(E)=2 n(D)=1  n2=n!n(S)! n(T)! n(R)! n(E)! n(D)!  n2=8!3! 2!=3360  p=100 n1n2=100 13360=5168=0.0298%

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Showing 6 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

Math student
why is n1 = 1?

n1 is the count of positive card (word DESSERTS) -> only one. n2 are the count of all combinations


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