Answer: There are 240 ways to arrange the letters in COMBINE if CN remain in their original order.
Step-by-step explanation: To arrange the letters in the word COMBINE, we need to use the formula for permutations, which is:
nPr = n! / (n-r)!
where n is the total number of items in the set, r is the number of items taken for the permutation, and ! means factorial.
Factorial of n is the product of all positive integers from 1 to n. For example, 5! = 5 x 4 x 3 x 2 x 1 = 120.
Since we have to keep the letters CN in their original positions, we can treat them as fixed and only consider the other five letters: O, M, B, I, E.
So, n = 5 and r = 5.
Plugging these values into the formula, we get:
5P5 = 5! / (5-5)!
= 5! / 0!
= 120 / 1
= 120
This means that there are 120 ways to arrange the five letters O, M, B, I, E.
However, we also have to account for the two positions of CN. Since CN can be either at the beginning or at the end of the word, we have to multiply the number of arrangements by 2.
So, the final answer is:
120 x 2 = 240
Therefore, there are 240 ways to arrange the letters in COMBINE if CN remain in their original order. Hope that this helps you out a lot! =)