Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 2)
2.
In how many different ways can the letters of the word 'LEADING' be arranged in such a way that the vowels always come together?
Answer: Option
Explanation:
The word 'LEADING' has 7 different letters.
When the vowels EAI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters LNDG (EAI).
Now, 5 (4 + 1 = 5) letters can be arranged in 5! = 120 ways.
The vowels (EAI) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
Video Explanation: https://youtu.be/WCEF3iW3H2c
Discussion:
97 comments Page 2 of 10.
Pema said:
1 decade ago
When it comes the question for arrangements, then it is a Permutation Or you all can remember it as keyword "PA" P=permutation and A=arrangement.
Likewise, for combination, it is all for selection purpose, remember keyword as "CS" c=combination,s=selection. Then apply formula for each. Easy.
Likewise, for combination, it is all for selection purpose, remember keyword as "CS" c=combination,s=selection. Then apply formula for each. Easy.
Mahanthesh said:
1 decade ago
Hi guys. As per the question, it s mentioned that all vowels should be together, but it has not been mentioned that it should be EAI. According to me these 3 vowels can be arranged in 3*2=6 ways. And the remaining letters LDNG can be arranged in 4*3*2*1= 24 ways. Can anyone explain me about this please ?
Jessie said:
1 decade ago
7 letter word = LEADING
CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD
SO NO. OF WORDS = L,(EAI),D,N,G = 5
permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5!
0! is assumed to be 1!)
EAI can be arranged among each other in = nPr = 3!/(3-3)= 3!
hence 5! x 3! = 120 x 6 = 720
CONDITION = VOWELS TO BE TOGETHER, HENCE (EAI) TO FOR A WORD
SO NO. OF WORDS = L,(EAI),D,N,G = 5
permuation to arrange 5 letters = nPr= n!/(n-r)!=5!/0!=5!
0! is assumed to be 1!)
EAI can be arranged among each other in = nPr = 3!/(3-3)= 3!
hence 5! x 3! = 120 x 6 = 720
(1)
Gopika S S said:
9 years ago
A number of permutations of "n" different things are taken "m" specified things always come together is m!* (n-m+1) !
Here the three vowels always come together. So here m is 3. A total number of letters is 7. Substitute we get.
3!* (7 - 3 + 1)! = 3! * 5!
= 6 * 120 =720.
Hope you got it.
Here the three vowels always come together. So here m is 3. A total number of letters is 7. Substitute we get.
3!* (7 - 3 + 1)! = 3! * 5!
= 6 * 120 =720.
Hope you got it.
Saravanakumar said:
7 years ago
LEADING.
Total vowels : E , A, I
remaining : LDNG
assume : EAI we can arrange (EAI)L, L(EAI), D(EAI), N(EAI),G(EAI)
so, total remaining is 4 so, 5!
and possibilities of arranging refer "assume" , 3!
then answer is : 5!*3!
120 * 6=720.
Total vowels : E , A, I
remaining : LDNG
assume : EAI we can arrange (EAI)L, L(EAI), D(EAI), N(EAI),G(EAI)
so, total remaining is 4 so, 5!
and possibilities of arranging refer "assume" , 3!
then answer is : 5!*3!
120 * 6=720.
(1)
Keerti AR said:
4 years ago
LEADING = 7 letters => 4 alphabets (LNDG) + 1 group (3 vowels) = 5 ! ways.
=>5 * 4 * 3 * 2 * 1 = 120.
Now, the group can be arranged in 3 ways, since there are 3 vowels,
So 3!=6 (3 * 2 * 1).
Hence, 120 * 6 = 720 ways can be arranged.
=>5 * 4 * 3 * 2 * 1 = 120.
Now, the group can be arranged in 3 ways, since there are 3 vowels,
So 3!=6 (3 * 2 * 1).
Hence, 120 * 6 = 720 ways can be arranged.
(32)
Shafi said:
1 decade ago
@Mahantesh,
You are correct 3! and 4!, because you spitted vowels and consonants,
But to combine them vowels+consonants.
i.e. (4 consonants + 1 set of vowels) = 5!
And (3 vowels {1 set}) = 3!
So 5!*3! = 5x4x3x2x1x3x2x1=720.
You are correct 3! and 4!, because you spitted vowels and consonants,
But to combine them vowels+consonants.
i.e. (4 consonants + 1 set of vowels) = 5!
And (3 vowels {1 set}) = 3!
So 5!*3! = 5x4x3x2x1x3x2x1=720.
Ameena said:
6 years ago
Hello,
We have word leading.we have vowels( EAI), first taken as 1 and can be arranged in _L_D_N_G_ that is in 5! Ways, EAI in 3! Ways, and LNDG in 4! ways.
That is 5! * 4! * 3! = 17,280 ways.
We have word leading.we have vowels( EAI), first taken as 1 and can be arranged in _L_D_N_G_ that is in 5! Ways, EAI in 3! Ways, and LNDG in 4! ways.
That is 5! * 4! * 3! = 17,280 ways.
(5)
Pavan@9966606261 said:
1 decade ago
@mayur.
You just look when ever you open the new exercise there will be availability of basic formulas. If you go through them half of the task would be finished easily. Have a good day buddy.
You just look when ever you open the new exercise there will be availability of basic formulas. If you go through them half of the task would be finished easily. Have a good day buddy.
Krishna said:
8 years ago
LEADING- vowels together in total 5 positions at L, E, A, D, and I.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
Ex. For the first position - (EAI) - (remaining 4 lettersLNGD) - 4! * 3!
For total 5 positions - 5*3!*4! -720.
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