How many different arrangements are there of the 10 letters in the word REGENERATE?
How many different arrangements are there of the 10 letters in the word REGENERATE in which the 4 Es are together and the 2 Rs have exactly 3 letters in between them?
Find the probability that a randomly chosen arrangement of the 10 letters in the word REGENERATE is one in which the consonants ( \(\mathrm { G } , \mathrm { N } , \mathrm { R } , \mathrm { R } , \mathrm { T }\) ) and vowels ( \(\mathrm { A } , \mathrm { E } , \mathrm { E } , \mathrm { E } , \mathrm { E }\) ) alternate, so that no two consonants are next to each other and no two vowels are next to each other. [5]
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