The letters of the word VOWEL are placed at random in a row The probability that the three consonant...........

Quantitative Aptitude (CDS) Probability

The letters of the word VOWEL are placed at random in a row. The probability that the three consonants come together is?

3/10

1/10

7/10

9/10

छोटे Courses बड़े Results

Master Probability

Prepare through Micro-courses

Try Now

Explanation:

The word VOWEL contains 5 distinct letters and they can be arranged at random in a row in 5P5 ways I.e in 5! = 120 ways.
Let us now consider those arrangements in which all the three consonants came together. So, in this case, we have to arrange two letters O, E and a pack of three consonants in a row which can be done in 3C3 I.e 3! = 6 ways
Also, the three consonants in their pack can be arranged in 3P3 = 3! = 6 ways.
Hence the number of arrangements in which the three consonants came together is 6×6=36 ways.
Therefore the probability that the consonants came together = 36/120
= 3/10