Question

In random arrangement of all letters of the word 'backlog'.find the probability that 2 voweld are together.

Answer 1

Given word is " backlog "
There are only two vowels { e.g., a and o}
there are five other latter { e.g., b, c , k , l and g }

Total number of possible way to arrange the latter = 7!
= 7 × 6 × 5 × 4 × 3 × 2 × 1
= 5040 ways

Two vowels comes together. It means { a ,o} assume a letter. so, number of rest latter = 7 - 1 = 6
number of arrangement of 6 latter = 6! Ways
we know two arrangement itself = 2! Ways .
so, number of arrangement of latter in this condition = 6! × 2! Ways
= 6 × 5 × 4 × 3 × 2 × 2
= 1440 ways

Now, probability = number of favourable outcomes/total number of possible outcomes
= 1440/5040 = 2 × 720/7 × 720 = 2/7

Hence, probability = 2/7