Question

Tammy is c choosing a 3 letter password from the letters a b c d and e the password can I have the same letter repeated in it how many passwords are possible coach of a softball team is holding tryouts and can only take two more players for the team there are seven players trying out how many different groups of two players can possibly be chosen

Answer 1

Explanation:

Problem One

If you are allowing duplicates, there are always a choice of five letters for the password. If you want to use 3 of them, then the answer is 5 * 5 * 5 = 125 possible passwords.

Problem Two

From 7 you must choose 2. You must cut out the duplicates AB is the same as BA

nCr

n = 7

r = 2

nCr = n! / (n - r)! r!

n! / (n - r)! r! = 7! / (7 - 2)! 2!

n! / (n - r)! r! = 7! / 5! 2!

7! / (5! 2!) = 7*6 * 5! / (5! ) 2!

7*6 / 2 = 21

There are 21 ways of choosing 2 plays from 7.