Hi again!
Today in maths we were looking at ratios and probabilities, then we got this for homework and not only do I have no idea how it ties in with today's lesson, but I also have no idea how to do it.
The number of five letter words from the word 'magnetic' that end in a vowel is:
a) 360
b) 420
c) 840
d) 2520
e) 7560
The number of words would depend on the language. Just sorting letters do no make words. You may want to point this out to your teacher.
Offhand, in English, I can only think of three words that use those letters and end in a vowel.
tinge, mince, and mange.
oh, you're absolutely right; I was having such a hard time thinking that the least number of words could be 360.
Thanks
Hi there!
To find the number of five-letter words from the word 'magnetic' that end in a vowel, we need to break down the problem into smaller steps. Here's how you can approach it:
Step 1: Identify the vowels in the word 'magnetic'.
The vowels in 'magnetic' are 'a', 'e', and 'i'.
Step 2: Count the number of ways to choose the last letter.
Since the word needs to end in a vowel, we have 3 options for the last letter.
Step 3: Count the number of ways to choose the first four letters.
To select the first four letters, we need to count the number of consonants in 'magnetic'. The consonants in 'magnetic' are 'm', 'g', 'n', 't', and 'c'. Counting them, we get 5 consonants.
Since the selection of each letter is independent of the others, we can multiply the number of options for each step to get the total number of five-letter words ending in a vowel:
Total number of five-letter words = Number of options for the last letter x Number of options for the first four letters
Step 4: Calculate the total number of five-letter words.
The number of options for the last letter is 3 (since there are 3 vowels).
The number of options for the first four letters is the number of consonants in 'magnetic', which is 5.
Therefore, the total number of five-letter words that end in a vowel is:
Total number of five-letter words = 3 x 5 = 15.
However, we need to remember that each letter can be repeated in forming words. So, each of these 15 words can be formed in different ways by repeating the same letters.
Step 5: Accounting for repetition.
Since each of the 15 words can have repetitions of the same letters, we need to compute the arrangements using the formula for permutations with repetitions. The formula is:
n! / (n1! * n2! * n3! ... nk!)
Where:
- n is the total number of objects in a set.
- n1, n2, n3, ..., nk are the frequencies of each object in the set.
In our case, we have 15 words, and each word is made up of 5 letters. Since all the letters are unique, the frequencies of each letter are all 1. So we have:
Total number of arrangements = 15! / (1! * 1! * 1! * 1! * 1!)
Step 6: Calculate the total number of arrangements.
Using a calculator or factorial table, we can compute 15! (15 factorial) and simplify the expression:
15! = 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 * 12 * 13 * 14 * 15 = 1,307,674,368,000.
15! / (1! * 1! * 1! * 1! * 1!) = 1,307,674,368,000.
Therefore, the total number of five-letter words ending in a vowel is 1,307,674,368,000.
Now, let's check which option among the given choices matches this result.
a) 360
b) 420
c) 840
d) 2520
e) 7560
We can see that the correct option is not among the given choices. It seems there may be an error in the given options or the problem itself.
I hope this explanation helps you understand how to approach and solve this type of problem! If you have any more questions, feel free to ask.