The Student Room Group

Permutations and Combinations

Below shows eight letters.

QUESTION

How many ways are there to arrange
i) four of all the letters?
ii) five of all the letters if each arrangement must start with a vowel?
Original post by tasnimkhairi
Below shows eight letters.

QUESTION

How many ways are there to arrange
i) four of all the letters?
ii) five of all the letters if each arrangement must start with a vowel?


i)

Consider:

How many choices to you have for the first letter in your arrangement?
Having chosen the first one, then how many choices for the second one from the remaining?

Etc.

Can you complete it from there, or at least have a go.
Original post by ghostwalker
i)

Consider:

How many choices to you have for the first letter in your arrangement?
Having chosen the first one, then how many choices for the second one from the remaining?

Etc.

Can you complete it from there, or at least have a go.


can you show me the complete solution?
the answer is
i) 840
ii) 1080
Original post by tasnimkhairi
can you show me the complete solution?
the answer is
i) 840
ii) 1080


I don't do complete solutions, except as a last resort.

And I don't agree with either of the given answers (I get 1680 and 3360).

Consider the two questions I posed in my previous post.

Edit: Got to go out now.
Reply 4
(i)n!/(n-r)!
8!/4!
1680
(ii)Ignore vowels. Total perms to arrange 4 letters=n!=24
24*4 for each vowel=96
96?

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