how many different ways can the letters in the word SOCIAL be arranged if the letter C must be directly followed by the letter I?
Answer: 720
Treat the CI as one item, so now you just have to arrange 5 items which is 5! or 120 ways, not 720
correct answer: 120
Well, let me entertain you with a little mathematical magic trick! Abracadabra!
Now, let's see. We have the word "SOCIAL" and we want the letter C to be directly followed by the letter I. So, before we start counting, let's place the CI duo next to each other, just to keep them happy.
Now we have "SO_CI_AL".
The remaining letters are S, O, A, and L.
We can arrange these 4 letters in 4! = 4 factorial ways (that's 4 x 3 x 2 x 1).
But hey, remember that sneaky CI duo? They can also be arranged in 2! = 2 factorial ways (that's 2 x 1).
So, multiplying the arrangement possibilities for the remaining letters by the arrangement possibilities for the CI duo, we get:
4! x 2! = 24 x 2 = 48.
Voila! There are 48 different ways that the letters in the word "SOCIAL" can be arranged if the letter C must be directly followed by the letter I. Enjoy the math magic show!
To find the number of different ways to arrange the letters in the word SOCIAL, with the condition that the letter C must be directly followed by the letter I, we can use the concept of permutations.
Let's start by treating CI as a single block. We can arrange the remaining letters (S, O, A, L) in 4! = 4 * 3 * 2 * 1 = 24 ways.
Now, within the CI block, the C and I can be arranged in 2! = 2 * 1 = 2 ways.
Therefore, the total number of different arrangements is 24 * 2 = 48.
So, there are 48 different arrangements of the letters in the word SOCIAL, where C is directly followed by I.
To find the number of different ways the letters in the word SOCIAL can be arranged, with the condition that the letter C must be directly followed by the letter I, we can use the concept of permutations.
Step 1: Count the total number of letters in the word SOCIAL. In this case, there are six letters.
Step 2: Determine the number of positions for the letter C. Since it must be directly followed by the letter I, we can fix the position of C, leaving us with five possible positions for the other letters.
Step 3: Calculate the number of ways the remaining five letters (O, S, I, A, L) can be arranged. This can be calculated by finding the permutations of five objects, which is equal to 5!.
Step 4: Multiply the number of positions for the letter C (1) by the number of ways the remaining letters can be arranged (5!). This gives us the total number of arrangements that satisfy the given condition.
1 * 5! = 1 * 5 * 4 * 3 * 2 * 1 = 120
Therefore, there are 120 different ways the letters in the word SOCIAL can be arranged, if the letter C must be directly followed by the letter I.