SOLUTION: Q:1- If we have first nine English alphabets from A to I and we have to arrange alphabets in such way that two consecutive vowels should not come together and three consecutive con

Question 1194928: Q:1- If we have first nine English alphabets from A to I and we have to arrange alphabets in such way that two consecutive vowels should not come together and three consecutive consonants should not come together. Find the total number of arrangements?
.
Hint: Arrangements for vowels are 1, 4, 7 or 2, 5, 8 or 3, 6, 9.

Q:2- If we do a little change in the arrangement of first nine English alphabets in such way that atleast four consecutive consonants must come together but six consecutive consonants and two consecutive vowels can not come together. Find the total number of arrangements?
.
Hint: Arrangement of vowels can be following:
1, 6, 8
1, 6, 9
1, 7, 9
1, 3, 8
1, 3, 9
1, 4, 9
In all these arrangements two vowels can not come together, six consunants can not come together but 4 or 5 consecutive consunants can come together.

Q:3- Can we define such topology T on some finite set X which is T³ but not To. Here To means Kolmogorov space and T³ is regular Hausdorff space.
Answer by ikleyn(52787) (Show Source): You can put this solution on YOUR website!
.

As I see from your post, you are a rare case of a universal student,

studying combinatorics and general topology at the same time.

I wish you success in your studies (!)

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