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Answer to Question #14490 in Statistics and Probability for denil

Question #14490
The letter of the word "SUCCESS" are in a row at random.Find the probability that all 'S' come together?
Expert's answer
Let N be a number of all different permutations of "SUCCESS".
As we have 3
letters 'S' and 2 letters 'C', then we should use
the formula for multinomial
coefficient:
N = 7! / (3! * 2!) = 420.

Now let's count the variants
that satisfy the problem:
1) SSS****;
2) *SSS***;
3) **SSS**;
4)
***SSS*;
5) ****SSS;
where * means 'C', 'U' or 'E'.

Using the same
principle, now we calculate the number of
all permutations of "UCCE"
string:
n = 4! / 2! = 12.

Finally, the probability that all S come
together is:
P = 5 * n / N = 5 * 12 / 420 = 1 / 7.

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