This set of Aptitude Questions and Answers (MCQs) focuses on “Permutations and Combinations”. These questions are beneficial for various competitive exams, placement interviews, and entrance tests.
1. In how many ways the letters of the word ‘CLEVER’ can be arranged?
a) 240
b) 720
c) 120
d) 360
View Answer
Explanation: The word ‘CLEVER’ has 6 letters. They are 1C, 1L, 2E’s, 1V and 1R.
Number of ways required = nPr = 6P4 = 6! / (1!)(1!)(2!)(1!)(1!) = 360.
The letters of the word can be arranged in 360 ways.
2. In how many different ways can the word ‘OCCUR’ be arranged, so that the vowels can come together?
a) 24
b) 6
c) 12
d) 10
View Answer
Explanation: The word ‘OCCUR’ has 5 letters.
We consider vowels in this word (OU) as 1 letter.
Now, we have CCR and (OU) i.e., 4(3 + 1) letters.
In CCR there are 2C’s and 1 R.
Number of ways we can arrange these letters = npr = 3p1 = 3! / 2! = 3.
There are 2 vowels, can be arranged = nPr = 2P1 = 2! / (1!)(1!) = 2.
Number of ways we can arrange so that vowels can come together = (3 * 2) = 6.
3. In how many ways a 4 digit number can be formed using 4, 2, 5, 7, 8?
a) 80
b) 24
c) 120
d) 5
View Answer
Explanation: Given, we have to find 4 digit numbers using 5 numbers.
Formula = nPr = 5P4 = 5! / (5 – 4)! = 5! / 1!.
5 * 4 * 3 * 2 * 1 = 120
4. How many ways 3 digit numbers can be formed using 2, 3, 4, 4, 5, 6?
a) 60
b) 120
c) 30
d) 80
View Answer
Explanation: Given, 2, 3, 4, 4, 5 and 6.
Formula = nPr = 6P3 = 6! / (6 – 3)! / (2!) = 6! / 3! / (2!) (The number ‘4’ is repeated so we use 2!).
(6 * 5 * 4 * 3 * 2 * 1) / (3 * 2 * 1) / (2 * 1) = 6 * 5 * 2 = 60
5. In how many different ways the word ‘CAREER’ can be arranged so that all the consonants will come together?
a) 12
b) 24
c) 8
d) 36
View Answer
Explanation: The word ‘CAREER’ has 6 letters.
We consider consonants in this word (CRR) as 1 letter.
Now, we have AEE and (CRR) i.e., 4(3 + 1) letters.
In ‘CRR’ there are 2R’s and 1C.
Number of ways we can arrange these letters = nPr = 4P2 = 4! / 2! = 12.
There are 2 Consonants, can be arranged = nPr = 3P1 = 3! / 2! = 2.
Number of ways we can arrange so that Consonants can come together = (12 * 3) = 36.
6. In how many ways the letters of the word ‘REDUCE’ can be arranged?
a) 120
b) 720
c) 360
d) 240
View Answer
Explanation: The word ‘REDUCE’ has 6 letters. They are 1R, 1E, 1D, 1U, 1C and 1E.
Number of ways required = nPr = 6P4 = 6! / (1!)(2!)(1!)(1!)(1!) = 360.
The letters of the word can be arranged in 360 ways.
7. In how many different ways the word ‘REGISTER’ be arranged, so that the vowels can come together?
a) 1080
b) 720
c) 1440
d) 1220
View Answer
Explanation: The word ‘REGISTER’ has 5 letters.
We consider vowels in this word (EIE) as 1 letter.
Now, we have RGSTR and (EIE) i.e., 6(5 + 1) letters.
In RGSTR there are 2R’s and 1G, 1S and 1T.
Number of ways we can arrange these letters = nPr = 6P4 = 6! / 2! = 360.
There are 3 vowels, 2E’s and 1’I’ can be arranged = nPr = 3P1 = 3! / (2!)(1!) = 3.
Number of ways we can arrange so that vowels can come together = (360 * 3) = 1080.
8. How many ways a 5 digit numbers can be formed using 2, 3, 5, 6, 3, 1, 8?
a) 2520
b) 1260
c) 840
d) 1080
View Answer
Explanation: Given that, we have to find 5 digit numbers using 7 numbers.
Formula = nPr = 7P5 = 7! / (7 – 5)! = 7! / 2! / 2! = 7! / (2! * 2!) (The number 3 is repeated so we use 2!).
7 * 6 * 5 * 2 * 3 = 1260
9. In how many the word ‘MAIZE’ can be arranged so that the consonants come together?
a) 12
b) 24
c) 48
d) 36
View Answer
Explanation: The word ‘ MAIZE’ has 6 letters.
We consider consonants in this word (MZ) as 1 letter.
Now, we have AIE and (MZ) i.e., 4(3 + 1) letters.
In ‘AIE’ there are 1’A’ and 1’I’ and 1’E’.
Number of ways we can arrange these letters = nPr = 4P3 = 4! / 1! = 24.
There are 2 Consonants, can be arranged = nPr = 2P1 = 2! / 1! = 2.
Number of ways we can arrange so that Consonants can come together = (24 * 2) = 48.
10. In how many ways the word ‘SITUATIONS’ can be arranged so that all the vowels can come together?
a) 10800
b) 9600
c) 8400
d) 12400
View Answer
Explanation: The word ‘SITUATIONS’ has 10 letters.
We consider vowels in this word (IUAIO) as 1 letter.
Now, we have STTNS and (IUAIO) i.e., 6(5 + 1) letters.
In STTNS there are 2S’s, 2T’s and 1N.
Number of ways we can arrange these letters = nPr = 6P4 = 6! / (2!)(2!) = 180 (Here, we have 2S’s and 2T’s so we use 2! * 2!).
There are 5 vowels, 2I’s, 1’U’, 1’A’, and 1’O’ can be arranged as = nPr = 5P3 5! / (2!) = 60.
Number of ways we can arrange so that vowels can come together = (180 * 60) = 1080.
More Aptitude Questions and Answers on Permutations and Combinations:
- Permutations and Combinations Questions (Set 2)
- Permutations and Combinations Questions (Set 3)
- Permutations and Combinations Questions (Set 4)
- Permutations and Combinations Questions (Set 5)
To practice all aptitude questions, please visit “1000+ Quantitative Aptitude Questions”, “1000+ Logical Reasoning Questions”, and “Data Interpretation Questions”.
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