Arranging the Letters of ‘Monday’ with a Vowel First

Arranging the Letters of 'Monday' with a Vowel First

The goal in this article is to determine the number of ways the letters of the word 'Monday' can be arranged such that the first letter is a vowel. This problem involves understanding permutations, specifically focusing on the vowels in the word.

Understanding the Problem

The word 'Monday' consists of 6 letters: M, O, N, D, A, Y. These letters include two vowels: A and O. Our task is to find how many arrangements of these letters there are when the first letter is specifically one of these vowels.

Approaching the Problem

We can break this problem down into two separate cases based on the first letter being either A or O. This division ensures we don't miss any possible arrangements.

Case 1: The First Letter is A

In this case, the remaining letters to arrange are M, O, N, D, Y. This gives us 5 letters to arrange. The number of permutations of 5 distinct items is given by 5 factorial (5!), which can be calculated as follows:

5! 5 × 4 × 3 × 2 × 1 120

Therefore, there are 120 ways to arrange the letters M, O, N, D, Y when A is the first letter.

Case 2: The First Letter is O

This situation is similar to the first case. If O is the first letter, the remaining letters to arrange are M, N, D, A, Y. Again, we have 5 distinct letters to arrange, giving us another 120 permutations.

So, for the second case, the number of permutations is also 120.

Calculating the Total Arrangements

To find the total number of arrangements where the first letter is a vowel, we simply add the permutations from both cases:

Total arrangements 120 (Case 1) 120 (Case 2) 240

Thus, there are 240 ways to arrange the letters of the word 'Monday' such that the first letter is a vowel.

Conclusion

In summary, if we want to arrange the letters of 'Monday' with a vowel in the first position, there are 240 distinct arrangements. This method can be applied to similar problems involving permutations and vowels in a word.

For those interested or curious about other word problems or permutations, consider exploring related topics such as combinatorics, graph theory, and advanced algebraic structures. Each of these fields offers fascinating insights into the intricacies of numbers and arrangements.