Aptitude - Permutation and Combination - Discussion

What is the answer if repetition is allowed?

The answer is correct. This is a permutation.

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

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.

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

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.

If repetition is allowed what is the answer?

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

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.

I agree @Ankur.

It is first we are selecting 4 letter from 10 letters.

i.e. C (10, 4) = 210.

Then arranging 4 letter in different ways. i.e. 4!= 24.

Therefore, it is selecting and arranging (combination of permutation and combination) =210 * 24 = 5040.

Firstly we have to check if any alphabet is repeated in the word "LOGARITHMS".

No, alphabets is repeated so it can be treated as any other general case. We are using permutation because it is not just the selection of 4 alphabets from the given word but the rearrangement of these alphabets in order to form a word (given: The words may or may not have any meaning). Now there are 10 alphabets & we must find out the number of 4 lettered words that can be formed which can be done in 10p4 ways. We need not multiply with 4! because have already considered the rearrangements (i.e usage of the concept of permutations).