Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 12)
12.
How many 4-letter words with or without meaning, can be formed out of the letters of the word, 'LOGARITHMS', if repetition of letters is not allowed?
Answer: Option
Explanation:
'LOGARITHMS' contains 10 different letters.
| Required number of words | = Number of arrangements of 10 letters, taking 4 at a time. |
| = 10P4 | |
| = (10 x 9 x 8 x 7) | |
| = 5040. |
Discussion:
68 comments Page 3 of 7.
AYYAJ said:
9 years ago
If repetition is allowed what is the answer?
Olamide said:
9 years ago
If repetition is allowed then it would be 10 * 10 * 10 * 10 = 10000.
Santhosh said:
9 years ago
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.
The no of the distinct permutations of the letters in the word"MISSISSIPPI" such that four I's do not come together.
Vidya said:
9 years ago
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.
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.
Navya said:
8 years ago
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).
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).
Navya said:
8 years ago
If the letters can be repeated then the answer would be 10^4.
Because if the word is _ _ _ _.
The 1st blank can be filled in 10 ways.
The 2nd blank can be filled in 10 ways again (since letters can be repeated).
Similarly, 3rd and 4th blanks can also be filled in 10 ways.
So, according to the fundamental principle the number of ways =10*10*10*10=10^4.
Because if the word is _ _ _ _.
The 1st blank can be filled in 10 ways.
The 2nd blank can be filled in 10 ways again (since letters can be repeated).
Similarly, 3rd and 4th blanks can also be filled in 10 ways.
So, according to the fundamental principle the number of ways =10*10*10*10=10^4.
Bmnt said:
8 years ago
What is the answer if repetition is allowed?
Satadru said:
8 years ago
If repetitions is allowed the formula would be 10^4.
Nithesh said:
8 years ago
There is not repetition getting, Logarithm all the words are different.
So permutations are taken.
Am I right?
So permutations are taken.
Am I right?
Chandu said:
10 years ago
What is the answer if repetition is allowed?
Post your comments here:
Quick links
Quantitative Aptitude
Verbal (English)
Reasoning
Programming
Interview
Placement Papers