4. a) An ice cream shop offers 25 flavors of ice cream and you can choose any 2
ID: 2908865 • Letter: 4
Question
4. a) An ice cream shop offers 25 flavors of ice cream and you can choose any 2 flavor. If you want you can choose to buy 2 scoop of same flavor ice-cream. How many ways are there to select 2 scoop from these 25 flavors? b) Now suppose you can't choose the same flavor twice. How many ways are there to select 2 different flavors from these 25 flavors? c) Now suppose the order of icecream scoop matters to you. How possible? 5. Suppose you want to open an online account in Twitter. They are asking you for an exactly 8 letter password. You can choose any small case letter from "a-z" and any number from 0-9. You cannot choose any letter or number more than once i. How many different passwords are possible to make? Is this a permutation problem or combination problem? Explain your answer ii. If twitter allows you to choose both small case letters, capital letters and any number between 0-9, how will "n" change compared to ()? Now how many passwords are possible to make.Explanation / Answer
4)
(a) If you want to buy 2 scoops of the same flavour, there are 25 possible ways of doing it.
(b) Same flavour cannot be chosen and order does not matter, the total ways = 25C2 = 25*24/2 = 300 ways.
(c) Since order matters, then the first flavour can be chosen from any of the 25 flavours and the secon can be chosen from any of the remaining 24 flavours. Therefore total ways = 25 * 24 = 600 ways.
5) 5(i) There are 26 small alphabets from a-z and 10 single digits from 0-9.
Therefore from a total of n = 26 + 10 = 36, we need to create an 8 letter password. Since we need to arrange these, it is a permutation problem.
The total passwords = 36P8 = 36!/(36-8)! = 36!/28! = 1.2201 * 1012.
(ii) n = 26 small case, 26 upper case and 10 single digits = 62
The total number of passwords = 62P8 = 62!/(62-8)! = 62!/54! = 1.36326 * 1014.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.