# 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.

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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