let n >= 5 be an integer, prove..
a) using algebra
b) using combinatorial argument
for part a) all you have to do is substitute 5 for n and you have:
but for part b) i have to make up a story.. need help please...
Hello memee4evaFor argument (b) here's the scenario: A password consists of characters. How many possible passwords are there, if characters are available to choose from, repetition being allowed?
Method 1
Each of the positions in the password can be filled in ways. There are therefore possible passwords.
Method 2
A If repetition is not allowed, there are ways of choosing which different characters to use; and ways of arranging them to form the password. There are therefore passwords where all three characters are different.
B If two characters are repeated, and the third one is different, there are ways of choosing which two characters will make up the password; then there are two ways of choosing which of these character is the one to be repeated; finally, there are then three ways of choosing the position to be occupied by the non-repeated character. So there are passwords that use two different characters.
C There are ways of choosing a single character, and therefore passwords made up of just one character.
The total number of passwords is therefore
Grandad