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26 Nov 2019, 00:52
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C
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Difficulty:
35%
(medium)
Question Stats:
75% (02:35) correct
25%
(02:19)
wrong
based on 194
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If the letters in the word ‘cucumber’ are rearranged in a random order, what is the probability that the new sequence of letters will begin and end with a vowel?
A. \(\frac{1}{4}\)
B. \(\frac{3}{8}\)
C. \(\frac{3}{28}\)
D. \(\frac{45}{56}\)
E. \(\frac{7}{8}\)
Are You Up For the Challenge: 700 Level Questions
A. \(\frac{1}{4}\)
B. \(\frac{3}{8}\)
C. \(\frac{3}{28}\)
D. \(\frac{45}{56}\)
E. \(\frac{7}{8}\)
Are You Up For the Challenge: 700 Level Questions
26 Nov 2019, 02:52
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CUCUMBER = 8!/2!* 2!
with condition ; U UCCMBR E
we can have the vowels in 3c2 ways
and other works in 6!/2! ways
so total P = 6!/2! / 8!/2!* 2! * 3c2
solve = \(\frac{3}{28}\)
IMO C
with condition ; U UCCMBR E
we can have the vowels in 3c2 ways
and other works in 6!/2! ways
so total P = 6!/2! / 8!/2!* 2! * 3c2
solve = \(\frac{3}{28}\)
IMO C
Bunuel
08 Oct 2021, 09:13
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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.
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.
