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# If the letters in the word ‘cucumber’ are rearranged in a random order

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Math Expert
Joined: 02 Sep 2009
Posts: 61339
If the letters in the word ‘cucumber’ are rearranged in a random order  [#permalink]

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25 Nov 2019, 23:52
00:00

Difficulty:

45% (medium)

Question Stats:

72% (03:00) correct 28% (02:19) wrong based on 18 sessions

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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. $$\frac{7}{8}$$

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Joined: 18 Aug 2017
Posts: 5885
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If the letters in the word ‘cucumber’ are rearranged in a random order  [#permalink]

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26 Nov 2019, 01:52
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

Bunuel wrote:
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
Re: If the letters in the word ‘cucumber’ are rearranged in a random order   [#permalink] 26 Nov 2019, 01:52
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