If two letters are taken at random from the word CANE, what is the probability that none of the letters would be vowels?

Question

If two letters are randomly taken one after the other from the word AUGUST, what is the probability that none of the letters would be vowels?

Answer 1

1/6

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Number of ways of selecting 2 letters of word CANE- 2*(3+2+1)=12
Number of ways selecting 2 vowels- 2 (CN & NC)
Probability- 2/12=1/6

Answer 2

• Two letters are taken randomly from out of the word "CANE"=12
• They are {(CA),(AC),(CN),(NC),(CE),(EC),(AN),(NA),(AE),(EA),(NE),(EN)}
• None of the letter is a vowel =2
• They are {(CN),(NC)}
  *So,
  =2/12
  =1/6
• The answer is 1/6