Arranging Letters in Mathematics

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SUMMARY

The discussion focuses on calculating the number of arrangements of the letters in the word "mathematics" that begin with a vowel and end with a letter other than 'h'. The word "mathematics" contains 11 letters, including 3 vowels (a, e, i). To solve the problem, one must select a vowel for the first position and then choose a letter for the last position from the remaining letters, excluding 'h'. The total arrangements can be calculated by determining the number of ways to fill the remaining 9 positions with the leftover letters.

PREREQUISITES
  • Understanding of permutations and combinations
  • Familiarity with the concept of vowels and consonants in English
  • Basic knowledge of factorial calculations
  • Ability to analyze letter arrangements in a word
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  • Study permutations with restrictions in combinatorial mathematics
  • Learn about factorial notation and its applications in counting arrangements
  • Explore the concept of combinations and how it differs from permutations
  • Practice problems involving arrangements of letters in various words
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Students studying combinatorial mathematics, educators teaching permutations, and anyone interested in solving arrangement problems in mathematics.

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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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