Question

The letters of the word "MOBILE" are arranged at random. Find the probability that the word so formed

i) starts with M
ii) starts with M
iii) ends with E. ​

Answer 1

The probability of the word 'MOBILE' starting with 'M' is 1/6. The probability of the word 'MOBILE' ending with 'E' is also 1/6.

Step-by-step explanation:

To find the probability that a word so formed starts with 'M', we need to consider the total number of possible arrangements and the number of arrangements that satisfy the given condition. The word 'MOBILE' has 6 letters, so there are 6! = 720 possible arrangements. To satisfy the condition of starting with 'M', we fix 'M' as the first letter and arrange the remaining 5 letters in 5! = 120 ways. Therefore, the probability of the word starting with 'M' is 120/720 = 1/6.

For the third condition, to find the probability that the word ends with 'E', we again consider the total number of possible arrangements and the number of arrangements that satisfy the given condition. We fix 'E' as the last letter and arrange the remaining 5 letters in 5! = 120 ways. Therefore, the probability of the word ending with 'E' is 120/720 = 1/6.