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 1 of 7.
VAIBHAV said:
6 years ago
10C4 *4!
10C4 = (10*9*8*7) / (4*3*2*1) =(10*3*7) = 210,
4! = 4 * 3 * 2 * 1 = 24.
So Obviously, 10C4 * 4! = 5040.
10C4 = (10*9*8*7) / (4*3*2*1) =(10*3*7) = 210,
4! = 4 * 3 * 2 * 1 = 24.
So Obviously, 10C4 * 4! = 5040.
(5)
CLIFORD said:
3 years ago
We select 4 letters from LOGARITHMS in 10C2 then we arrange the 4 letters in four factorials.
(2)
Aop said:
3 years ago
We use permutation for selection and arranging.
They asked two processes in question.
step 1: Selection- to select 4 letters from 10 letters,
step 2: Arranging- to arrange 4 letters in different ways.
Why use arranging?
Because, by arranging the 4 words in different ways we can get many words, which can be meaningful or non-meaningful.
So, for permutation = n!/(n-1)!
They asked two processes in question.
step 1: Selection- to select 4 letters from 10 letters,
step 2: Arranging- to arrange 4 letters in different ways.
Why use arranging?
Because, by arranging the 4 words in different ways we can get many words, which can be meaningful or non-meaningful.
So, for permutation = n!/(n-1)!
(2)
Sahithya said:
1 decade ago
10C4 means 10x 9 x 8 x 7/ (1 x 2 x 3 x 4).
10P4 means 10 x 9 x 8 x 7.
As we are considering order we hav to use permutations.
10P4 means 10 x 9 x 8 x 7.
As we are considering order we hav to use permutations.
(1)
Pancy said:
4 years ago
@Shashwat.
When we select the things and then arrange them then we use permutations.
But when we only have to select then we use combinations.
In the above question we are selecting and arranging them too that's the reason we use permutations.
When we select the things and then arrange them then we use permutations.
But when we only have to select then we use combinations.
In the above question we are selecting and arranging them too that's the reason we use permutations.
(1)
Ninad S Nagpure said:
6 years ago
If repetition is allowed then the answer is 10^4=10000!.
The no of possible letters to occupy each of the four spaces is 10.
_ _ _ _
10*10*10*10.
If repetition is not allowed,
10*9*8*7.
The no of possible letters to occupy each of the four spaces is 10.
_ _ _ _
10*10*10*10.
If repetition is not allowed,
10*9*8*7.
(1)
Mijanul said:
6 years ago
nCr = ( 1 / r! ) * nPr.
nPr = r! * nCr.
That's why here nPr (permutation) is used.
nPr = r! * nCr.
That's why here nPr (permutation) is used.
(1)
Akash kumar said:
6 years ago
if repetition allowed then how to solve it? Please tell me.
(1)
Pradeep said:
1 decade ago
Its very easy, no need to get confused with permutation.
Divide the statement in two part.
From given 10 character, we have to choose 4 of them only.
So, 10C4 = 10*9*8*7/4! = 210.
Now we have to arrange there 4 character.
So, it would be simply 4! because there is no repetition of word.
Total - 210*24 = 5040.
Moral - choose 4 word out of 10 then arrange them by 4!.
Divide the statement in two part.
From given 10 character, we have to choose 4 of them only.
So, 10C4 = 10*9*8*7/4! = 210.
Now we have to arrange there 4 character.
So, it would be simply 4! because there is no repetition of word.
Total - 210*24 = 5040.
Moral - choose 4 word out of 10 then arrange them by 4!.
(1)
Akash said:
1 decade ago
What does the exclamation mark imply? please can someone explain this question?
(1)
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