Exercise :: Permutation and Combination - General Questions
- Permutation and Combination - Important Formulas
- Permutation and Combination - General Questions
| 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 A Explanation:
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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? |
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Answer: Option C Explanation: 'LOGARITHMS' contains 10 different letters.
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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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Answer: Option C 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.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
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Number of ways of arranging these letters =| 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.
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