Wrong bro...if u take all S as 1 thn total arrngmnt in which S come together= 7!4! so prbabilty of arnmnt in which S don't come togthr = 1-[(7!4!)÷10!]=29/30

Problem Analysis:
To find the probability that all S's don't come together, we need to analyze the different possible arrangements of the word MISSISSIPPI. We will then count the number of favorable arrangements where the S's are not together, and divide it by the total number of possible arrangements.

Possible Arrangements:
The word "MISSISSIPPI" has a total of 11 letters, with 4 I's, 4 S's, and 2 P's. To calculate the total number of possible arrangements, we can use the concept of permutations. The formula for permutations is given by n! / (n1! * n2! * ... * nk!), where n is the total number of objects and n1, n2, ..., nk are the counts of each distinct object.

In this case, we have:
- n = 11 (total number of letters)
- n1 = 4 (count of I's)
- n2 = 4 (count of S's)
- n3 = 2 (count of P's)

Using the permutation formula, we can calculate the total number of possible arrangements as:
Total arrangements = 11! / (4! * 4! * 2!)

Favorable Arrangements:
To count the number of favorable arrangements where the S's are not together, we can consider the S's as distinct objects and the remaining letters as distinct objects as well. We can then calculate the number of arrangements of these distinct objects.

First, we need to find the number of ways the S's can be arranged. Since there are 4 S's, there are a total of 4! = 24 arrangements of the S's.

Now, let's consider the remaining letters (M, I, I, I, P, P). We have 7 distinct objects, which can be arranged in 7! = 5040 ways.

Since the S's can be arranged in 24 ways and the remaining letters can be arranged in 5040 ways, the total number of favorable arrangements is:
Favorable arrangements = 24 * 5040

Probability Calculation:
To find the probability that all S's don't come together, we divide the number of favorable arrangements by the total number of possible arrangements:

Probability = Favorable arrangements / Total arrangements

Now, we can substitute the values we calculated earlier to find the probability.