Question

Find the probability that in a random arrangement of the letters of the word 'SOCIAL' vowels come together.

Answer 1

Number of Vowels in word 'SOCIAL' are A,I,O

Number of ways we can arrange SOCIAL, word with vowels together is SCL(AIO) = $4!\times 3!$

Total number of arrangements are 6!

Probability $=\frac{4!\times 3!}{6!}=\frac{4!\times 3\times 2}{6\times 5\times 4!}=\frac{1}{5}$