Aptitude - Permutation and Combination - Discussion

I have a problem can anyone help me to solve this.

The no of the distinct permutations of the letters in the word"MISSISSIPPI" such that four I's do not come together.

If repetition is allowed then it would be 10 * 10 * 10 * 10 = 10000.

If repetition is allowed what is the answer?

Easier method.

Here, repetition is not allowed. So, to form a word of 4 letters. _ _ _ _.

The 1st letter can be chosen out of 10 letters.

The 2nd letter can be chosen out of the remaining 9 letters. (since no repetition & 1 letter is filled in the 1st position).

The 3rd letter can be chosen out of the remaining 8 letters.

The 4th letter can be chosen out of the remaining 7 letters.

Thus, 10 * 9 * 8 * 7 = 5040.

They mentioned that no repetition are allowed then how could we use permutations here?

Here first, we can use 10C4 to find no.of groups containing 4 words. Then by multiplying by !5 we will obtain no.of word arrangements in those groups. In question we have to find words.

The answer is correct. This is a permutation.

i.e npr=n!/(n-r)! Here n! is 10, r is 4.

What is the answer if repetition is allowed?

Why permutation here?

Logarithms ===> total = 10 alphabets.

We have to form 4-letter words, without repeating the letters. We have place for 4 alphabets.

In 1st blank, out of 10, anyone of it can come, so we have 10 choices ---> 10.

In 2nd blank, now, 9 letters are left, out of 9 you can choose one ----> 10*9.

In 3rd blank, now 8 left, i.e. ---> 10*9*8.

In 4th blank, any remaining of 7 letters can come ---> 10*9*8*7 = 5040.

Here we are using --- Logarithms --- word which contain different alphabets.

If it contain one or two alphabets more then one time then above solution is applicable.

Solve this example in place of Logarithms use logarithm. Please solve this.