In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. ### Exercise :: Permutation and Combination - General Questions View Answer Discuss in Forum Workspace Report
View Answer Discuss in Forum Workspace Report
13. |
In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
| A. | 10080 | B. | 4989600 | C. | 120960 | D. | None of these | 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.
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. |
#### Page 2 ### Exercise :: Permutation and Combination - General Questions View Answer Discuss in Forum Workspace Report
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.
Required number of numbers = (1 x 5 x 4) = 20. | View Answer Discuss in Forum Workspace Report
Didn't get the answer. Contact people of Talent-Aptitude directly by clicking here |