Under the intended interpretation: three of the eight letters are vowels, so when we arrange them randomly, the probability is 3/8 that the first letter is a vowel, and then is 2/7 that the last letter is also a vowel, so the probability both are vowels is (3/8)(2/7) = 3/28.
That's assuming we're just arranging the letters randomly. But the question says "rearranged", instead of "arranged", which makes it sound like we are obligated to change the order of the letters from CUCUMBER to something else. That's not what's meant (if it were, the right answer isn't among the choices) but if that's what we were doing here, then you'd need to follow the method outlined in Archit's solution, but subtract one in the denominator to exclude the original order.
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