Final answer:
The number of different permutations of the letters in the word 'MONDAY' where the two vowels are not together is 480.
Explanation:
To find the number of different permutations where the two vowels are not together in the word 'MONDAY,' we can first calculate the total number of ways to arrange the letters and then subtract the cases where the vowels are together. The word 'MONDAY' has 6 letters, with 2 vowels ('O' and 'A') and 4 consonants ('M', 'N', 'D', 'Y').
We can calculate the total number of permutations by arranging the 4 consonants first in 4! ways, and then inserting the 2 vowels in the gaps between consonants, giving us 5 possible positions ('_M_N_D_Y_'). The vowels can be placed in these positions in 5P2 = 5!/(5-2)! = 54 = 20 ways.
Therefore, the total number of permutations where the two vowels are not together in 'MONDAY' is 4! 20 = 480 different ways.
Learn more about Permutations and Vowels here:
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