Exercise :: Permutation and Combination - General Questions
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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? | |||||||||||||||
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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Exercise :: Permutation and Combination - General Questions
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7. | 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? |
Answer: Option 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. |
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