The tinyurl.com service lets you alias a long URL to a shorter one. For example,

Question

The tinyurl.com service lets you alias a long URL to a shorter one. For example, you can ask the service to send people to

http://www.expensive.edu/departments/math/hard/discrete/

when they enter the URL http://tinyurl.com/sd8k4 in a web browser.

(a) How many different URLs of the form http://tinyurl.com/***** are possible, if ***** can be any string of the characters a, b, ..., z, and 0, 1, ..., 9? (Repeated characters are allowed.)


(b) How many different URLs of the form http://tinyurl.com/***** are possible, if ***** must be a string consisting of three letters (a, b, ..., z) followed by two digits (0, 1, ..., 9)? (Repeats allowed.) For example, ace44, cub98.


(c) Suppose that an arbitrary string ***** of letters and digits (as in subpart (a)) is chosen at random. What is the probability that this string contains no letters? (Round your answer to four decimal places.)

Explanation / Answer

a). For any place we have 26 alphabets (a-z) and 10 numbers(0-9)=36 distinct characters. Now in total we have 5 places and since repeatation is allowed. So we have (36^5)= 60466176

b).For first three places we have 26 alphabets as choice and for the next two we have 10 numbers as choice.(repeatation allowed).

So we have =(36^3)*(10^2) = 4665600

C).Probability = favoured outcomes/total outcomes

Favourable outcomes = no letters in string meaning no alphabets.

=10^5

=100000

Total outcomes is as given in part (a).

Probability=(100000/60466176)

=0.0016538.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.