Arranging Letters in Mathematics

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The discussion focuses on calculating the arrangements of the letters in "mathematics" that start with a vowel and end with a letter other than 'h'. The word contains 11 letters, with specific vowels available for the first position. After selecting a vowel for the first position, the remaining letters must be arranged in the remaining spaces, ensuring the last letter is not 'h'. The problem emphasizes the importance of determining the available letters for both the starting and ending positions to find the total arrangements. The approach involves combinatorial reasoning to solve the arrangement challenge.
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How many arrangements of the letters in the word mathematics begin with a vowel and end with a letter other than h?


Please help!
 
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CanadianEh said:
How many arrangements of the letters in the word mathematics begin with a vowel and end with a letter other than h?


Please help!

How would you go about approaching this problem? I assume the arrangements of letters do not have to make real words from the dictionary? Do all the words have to be the same length as the word mathematics?
 
MATHEMATICS

so you have 11 letters.


_ _ _ _ _ _ _ _ _ _ _
1 2 3 4 5 6 7 8 9 10 11 (letter position)

Each space for each letter.

You want position 1 to be a vowel. How many vowels do you have? So for position 1, how many ways can you select a vowel to start this arrangement? So in position 1, write down the number of vowels you can choose from.

By writing the number of vowels you can start with, you have in essence chosen a vowel to start with. How many letters are left to choose from? (This includes h).

Hence in position 11, how many letters can you put there excluding h?

Now how many letters do you have left? How many ways can you arrange the rest of letters in the remaining 9 spaces?
 

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