Aptitude - Permutation and Combination - Discussion
Discussion Forum : Permutation and Combination - General Questions (Q.No. 5)
5.
In how many ways can the letters of the word 'LEADER' be arranged?
Answer: Option
Explanation:
The word 'LEADER' contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
 Required number of ways = |
6! | = 360. |
| (1!)(2!)(1!)(1!)(1!) |
Video Explanation: https://youtu.be/2_2QukHfkYA
Discussion:
84 comments Page 6 of 9.
Swapnil said:
1 decade ago
In this letter e repeated twice.
So that in permutation swapping of e letter.
Does not form new word and so they are counted.
Once at every case so divided by 2!.
So that in permutation swapping of e letter.
Does not form new word and so they are counted.
Once at every case so divided by 2!.
Mancy said:
1 decade ago
Hi @Thokie,
Q: There are 9 switches in a fuse box, how many different arrangements are there?
Ans: 2 2 2 2 2 2 2 2 2.
Each switch has two possible, on or off placing a 2 in each of the 9 position.
So, we have
2 raise to the power 9 = 512.
So it means there are 512 different arrangements can be done.
Hope this'll help.
Q: There are 9 switches in a fuse box, how many different arrangements are there?
Ans: 2 2 2 2 2 2 2 2 2.
Each switch has two possible, on or off placing a 2 in each of the 9 position.
So, we have
2 raise to the power 9 = 512.
So it means there are 512 different arrangements can be done.
Hope this'll help.
Thokie said:
1 decade ago
There are 9 switches in a fuse box, how many different arrangements are there?
Sankari said:
1 decade ago
In how many ways ELECTION can be arranged so that the vowels occupy the odd places.
Ashwini said:
1 decade ago
Hi @Pavithra the word LEADER has repeated letter 'E' twice so 6!/2! = 6*5*4*3 = 360.
Pavithra said:
1 decade ago
Why we should take like 6*5*4*3?
Vikram said:
1 decade ago
360 is the correct answer because "C" is repeated
6!/2! = 6*5*4*3 = 360.
6!/2! = 6*5*4*3 = 360.
Harish said:
1 decade ago
In how many different way can the letters of the word CREAM arranged.
Sundar said:
1 decade ago
In how many different ways can the letters of the word 'ORANGE' be arranged so that the three vowels never come together ?
Answer :
The total number of ways of arranging ORANGE = 6!
The total number of ways o,a and e can be arranged = 3!
The total number of groups when the vowels are one group and the rest are individuals= 4!
= 6! - 4! x 3!
= 576
In how many different ways can the letters of the word 'EXTRA' be arranged so that the two vowels never come together ?
Answer:
The total number of ways of arranging EXTRA = 5!
The total number of ways e and a can be arranged = 2!
The total number of groups when the vowels are one group and the rest are individuals XTR(EA) = 4!
= 5! - 4! x 2!
= 72
Answer :
The total number of ways of arranging ORANGE = 6!
The total number of ways o,a and e can be arranged = 3!
The total number of groups when the vowels are one group and the rest are individuals= 4!
= 6! - 4! x 3!
= 576
In how many different ways can the letters of the word 'EXTRA' be arranged so that the two vowels never come together ?
Answer:
The total number of ways of arranging EXTRA = 5!
The total number of ways e and a can be arranged = 2!
The total number of groups when the vowels are one group and the rest are individuals XTR(EA) = 4!
= 5! - 4! x 2!
= 72
Jonathan said:
1 decade ago
LEADER
One way of arranging this is
"EADERL" (The first 'E' and the second 'E')
If I want to put the second 'E' in place of the first 'E' to make another arrangement, I would get
"EADERL" which is the same as the previous one.
POINT: we have shown that eventhough I interchange the first 'E' and the second 'E', we came up with the same arrangement.
MEANING... if there are TWO same letters, there will be DUPLICATION...
That is the reason why we DIVIDE by TWO!
It's not 5! because still, there are six letters we are arranging!
Hope this insight can help you!:)
One way of arranging this is
"EADERL" (The first 'E' and the second 'E')
If I want to put the second 'E' in place of the first 'E' to make another arrangement, I would get
"EADERL" which is the same as the previous one.
POINT: we have shown that eventhough I interchange the first 'E' and the second 'E', we came up with the same arrangement.
MEANING... if there are TWO same letters, there will be DUPLICATION...
That is the reason why we DIVIDE by TWO!
It's not 5! because still, there are six letters we are arranging!
Hope this insight can help you!:)
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