This Article consist of most important ” Permutation and Combination Questions and Answers ” topic that are mostly asked in all competitive exams. We collected these questions from the students who appeared in exams. Now try to solve these questions.
Permutation and Combination Questions and Answers
Question : 1 In how many different ways can the letters of the word ‘DETAIL’ be arranged in such a way that the vowels occupy only the odd positions?
A. 32
B. 48
C. 36
D. 60
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Correct Answer : C
Explanation :
There are 6 letters in the given word, out of which there are 3 vowels and 3 consonants.
Let us mark these positions as under:
(1) (2) (3) (4) (5) (6)
Now, 3 vowels can be placed at any of the three places out 4, marked 1, 3, 5.
Number of ways of arranging the vowels = 3P3 = 3! = 6.
Also, the 3 consonants can be arranged at the remaining 3 positions.
Number of ways of these arrangements = 3P3 = 3! = 6.
Total number of ways = (6 x 6) = 36
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Question : 2 How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
A. 5
B. 10
C. 15
D. 20
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Correct Answer : D
Explanation :
Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
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Question : 3 In how many ways can the letters of the word ‘LEADER’ be arranged?
A. 72
B. 144
C. 360
D. 720
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Correct Answer : C
Explanation :
The word ‘LEADER’ contains 6 letters, namely 1L, 2E, 1A, 1D and 1R.
Required number of ways = 6!/(1!)(2!)(1!)(1!)(1!)
=360
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Question : 4 In how many different ways can the letters of the word ‘CORPORATION’ be arranged so that the vowels always come together?
A. 810
B. 1440
C. 2880
D. 50400
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Correct Answer : D
Explanation :
In the word ‘CORPORATION’, we treat the vowels OOAIO as one letter.
Thus, we have CRPRTN (OOAIO).
This has 7 (6 + 1) letters of which R occurs 2 times and the rest are different.
Number of ways arranging these letters = 7!/2! = 2520.
Now, 5 vowels in which O occurs 3 times and the rest are different, can be arranged
in 5!/3! = 20 ways.
Required number of ways = (2520 x 20) = 50400
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Question : 5 In how many different ways can the letters of the word ‘LEADING’ be arranged in such a way that the vowels always come together?
A. 360
B. 480
C. 720
D. 5040
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Correct Answer : C
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
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