Probability question - random placement of alphabets

[hgupta]

hello, i could never work out this problem, and i am fed up it now,

 

Given a word "ARTICLE", its alphabets are jumbled up and then placed at random. What is the probability that the vowels will end up taking even places?

 

hope my question is clear!!

 

thank you

[Sisyphus]

 

 

hope my question is clear!!

 

 

Not really. You mean what is the probability that the vowels will be in the 2nd, 4th and 6th positions? If so, just do what needs to happen one letter at a time.

 

The first letter has to be a consonant. Probability 4/7.

 

The next letter has to be a vowel, and you have 3 of each left. Hence, probability 3/6 (or simplified to 1/2), assuming the first letter is already in place.

 

Third letter consonant, of which 3 of your remaining 5 letters are. Probability is 3/5.

 

Then 2/4 (or 1/2), 2/3, 1/2, and finally 1/1, since it's your last letter and there's no other option.

 

Then just multiply each probability together for the probability of all them happening.

 

4/7 * 1/2 * 3/5 * 1/2 * 2/3 * 1/2 *1/1 = 24/840, which simplifies to 1/35. That's your answer.

[hgupta]

hehe, thank you!!

 

actually did 3/7 for the second alphabet (or first vowel) !!