Aptitude - Permutation and Combination
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OverviewExercise"Everything you can imagine is real."
- Pablo Picasso
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| 11. |
In how many ways can a group of 5 men and 2 women be made out of a total of 7 men and 3 women?
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Answer: Option D
Explanation:
| Required number of ways = (7C5 x 3C2) = (7C2 x 3C1) = |
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7 x 6 |
x 3 |
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= 63. |
| 2 x 1 |
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| 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 D
Explanation:
'LOGARITHMS' contains 10 different letters.
| Required number of words |
= Number of arrangements of 10 letters, taking 4 at a time. |
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= 10P4 |
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= (10 x 9 x 8 x 7) |
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= 5040. |
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| 13. |
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
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| A. |
10080 | B. |
4989600 | | C. |
120960 | D. |
None of these |
Answer: Option E
Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
 Number of ways of arranging these letters = |
8! |
= 10080. |
| (2!)(2!) |
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
| Number of ways of arranging these letters = |
4! |
= 12. |
| 2! |
Required number of words = (10080 x 12) = 120960.
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| 14. |
In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
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Answer: Option B
Explanation:
The word 'OPTICAL' contains 7 different letters.
When the vowels OIA are always together, they can be supposed to form one letter.
Then, we have to arrange the letters PTCL (OIA).
Now, 5 letters can be arranged in 5! = 120 ways.
The vowels (OIA) can be arranged among themselves in 3! = 6 ways.
Required number of ways = (120 x 6) = 720.
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