Using the ordinary alphabet and allowing repeated letters, find the number of words of length 8 that have at least one C.
What's the difference between the wording of "exactly one" and "atleast one"?
at least 1 means any integer bigger than zero
I think surely you know what exactly 1 means ...
The wording "exactly one" means that there must be exactly one instance of the specified element. In this case, "exactly one C" would mean that the word should have only one occurrence of the letter C.
On the other hand, the wording "at least one" means that there should be at least one instance of the specified element. In this case, "at least one C" would mean that the word could have one or more occurrences of the letter C.
To find the number of words of length 8 that have at least one C using the ordinary alphabet and allowing repeated letters, we can use the principle of complement. We first find the total number of words without any restriction, and then subtract the number of words with no C's.
Here are the steps to find the number of words of length 8 with at least one C:
Step 1: Calculate the total number of words of length 8 using the ordinary alphabet.
To calculate the total number of words of length 8, we can raise the number of letters in the alphabet to the power of 8 (since there are 8 positions to fill in the word) since we can choose any letter from the alphabet for each position.
If we assume an alphabet of 26 letters (English alphabet), then the total number of words of length 8 is 26^8.
Step 2: Calculate the number of words of length 8 with no C's.
To calculate the number of words without any C's, we have to place any of the remaining 25 letters (excluding C) in each of the 8 positions. Hence, the number of words of length 8 with no C's is 25^8.
Step 3: Subtract the number of words with no C's from the total number of words.
The number of words of length 8 with at least one C is obtained by subtracting the number of words with no C's from the total number of words. Hence, the final count is 26^8 - 25^8.
By evaluating this expression, we can find the number of words of length 8 that have at least one C using the ordinary alphabet and allowing repeated letters.