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 2 of 7.
Vidya said:
8 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.
Krishna Kumar said:
7 years ago
Formula for Permutation nPr= n!/(n-r!)
For 10P4= 10!/(10-4!).
=> 10!/6!.
=>10x9x8x7x6x5x4x3x2x1
--------------------------------------
6x5x4x3x2x1
=>6x5x4x3x2x1 in both numerator and denominator will get cancelled.
Hence 10x9x8x7=5040.
For 10P4= 10!/(10-4!).
=> 10!/6!.
=>10x9x8x7x6x5x4x3x2x1
--------------------------------------
6x5x4x3x2x1
=>6x5x4x3x2x1 in both numerator and denominator will get cancelled.
Hence 10x9x8x7=5040.
Lydia said:
1 decade ago
It can also be done in another way.
Number of ways of selecting 4 letters from 10 letters=10C4
=(10*9*8*7)/4!
Number of ways of arranging these 4 letters =4P4=4!
So, total number of words formed= [(10*9*8*7)/4!]*4! = 10*9*8*7 = 5040
Am I correct?
Number of ways of selecting 4 letters from 10 letters=10C4
=(10*9*8*7)/4!
Number of ways of arranging these 4 letters =4P4=4!
So, total number of words formed= [(10*9*8*7)/4!]*4! = 10*9*8*7 = 5040
Am I correct?
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)
Shivam said:
1 decade ago
I'm confused for in which question we do permutation and combination. I have used combination in this question but I was wrong. But some other questions which as same as this question solved by combination. Why did you use permutation on this?
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)
Rishi said:
9 years ago
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.
Habib said:
1 decade ago
It's said 4 letters , and they dont repeat.!!!!.......
Then how come permutations..which actually implies arrangement of the selected letters at a time...
Pls help me, if i am wrong
Then how come permutations..which actually implies arrangement of the selected letters at a time...
Pls help me, if i am wrong
(1)
Prawin said:
1 decade ago
It is a four letter word ---- out of 10 repeatition is not allowed so first 10 we have 1 then out of nine wehave 1then out of 8 we have 1 then out of 7 we have 1 so 10*9*8*7=ans
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)
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