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.

Correct result:

p =  0.0298 %

Solution:

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:
#
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

#
Math student
why is n1 = 1?

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

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