In how many ways can the letter of the word SECTION be arranged if the consonants must always be in the order in which they occur in the word itself?
wrong its 210
S E C T I O N
Total number of letters = 7!
# of consonants is 4! (S,c,t,n)
7!/4!= 210
Don't know why, that's just what the back of the book says :s
Well, let's analyze this conundrum, shall we? The word "SECTION" has seven letters, out of which five are consonants (S, C, T, N) and two are vowels (E, I). Now, since the consonants need to stay in the same order, we only need to focus on the arrangement of the vowels.
There are two vowels, which means we have two options for the first vowel and only one option left for the second vowel. Therefore, the number of ways we can arrange the two vowels is 2 x 1 = 2.
But wait, don't be too quick to celebrate. We need to take into consideration that the vowels could swap positions and still have the same arrangement. So, we have to multiply the previous result by 2 to account for this possibility.
Hence, the total number of ways to arrange the letters of the word "SECTION" while keeping the consonants in their original order is 2 x 2 = 4.
So, dear friend, there are four ways to arrange the letters of the word "SECTION." That's enough arrangements to keep a clown like me entertained for a while!
To find the number of ways to arrange the letters in the word SECTION, while keeping the consonants in their original order, we can follow these steps:
Step 1: Identify the consonants and vowels in the word SECTION.
- The consonants are S, C, T, N
- The vowels are E, I, O
Step 2: Determine the number of ways to arrange the vowels.
- There are three vowels, E, I, and O.
- The number of ways to arrange three items is 3! (3 factorial), which is equal to 3 x 2 x 1 = 6.
Step 3: Determine the number of ways to arrange the remaining consonants.
- The remaining consonants are S, C, and T.
- The number of ways to arrange three items is 3! (3 factorial), which is equal to 3 x 2 x 1 = 6.
Step 4: Multiply the number of ways to arrange the vowels and consonants.
- The number of ways to arrange the vowels (6) * the number of ways to arrange the consonants (6) = 36.
So, there are 36 ways to arrange the letters in the word SECTION while keeping the consonants in their original order.
thank you
without restrictions there would be 7! ways or 5040
The EIO can be arranged in 3! or 6 ways, but we want only one of these sequences.
so the number of arrangements is 5040/6 = 840
(somebody check my thinking on this)