Study the given set of alphabets carefully and answer the following qu...
The given set of alphabets is: S N T A O U B F P V C G Q W D H R X E Z Q.
To find the maximum number of four-letter words that can be made using the letters of the word TRAINER, we need to analyze the given set of alphabets and identify the number of occurrences of each letter in TRAINER.
The word TRAINER contains the letters T, R, A, I, N, and E. Let's count the number of occurrences of each letter in TRAINER:
- T: 2
- R: 2
- A: 1
- I: 1
- N: 1
- E: 1
Now, we can calculate the maximum number of four-letter words that can be formed using these letters. To do this, we will use the concept of permutations.
The formula to calculate the number of permutations of n objects taken r at a time is given by nPr = n! / (n - r)!
In this case, we have 7 different letters (T, R, A, I, N, E) and we want to form four-letter words.
Using the formula, we can calculate the number of permutations as follows:
7P4 = 7! / (7 - 4)! = 7! / 3! = (7 x 6 x 5 x 4 x 3 x 2 x 1) / (3 x 2 x 1) = 840
Therefore, the maximum number of four-letter words that can be made using the letters of the word TRAINER is 840.
Now, let's compare the options provided:
a. > 20 - Incorrect, as the maximum number of four-letter words is 840, which is greater than 20.
b. between 10 and 20 - Incorrect, as the maximum number of four-letter words is 840, which is greater than 20.
c. <3 -="" incorrect,="" as="" the="" maximum="" number="" of="" four-letter="" words="" is="" 840,="" which="" is="" greater="" than="">3>
d. = 10 - Incorrect, as the maximum number of four-letter words is 840, which is not equal to 10.
Therefore, the correct answer is option B - between 10 and 20.
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