Question

John is choosing a password for his access to the internet. He decided not to use the digit 0 or the
letter M. Each letter or number may be used more than once. How many passwords of 2 letters followed
by 4 digits are possible?--- is there a formula for this? or a way to plug it into the calculator?

Answer 1

two letter part:
there are 25 letters used
total possibilities for this = no. of permutations of 2 out of 25 = 25*24

Answer 2

ooops - the letters can be used more than once so we must add 25 to the above

Answer 3

it is the counting principle

Answer 4

the above is a quick way of doing it the formula is

number of permutations r from n = n! / (n-r)!

Answer 5

yes

Answer 6

25 letters, 9 digits,
\(25\times 25\times 9\times 9\times 9\)

Answer 7

The choice for the no. of ways in which the first two letters can be chosen from available 25 letters = 25P2 = 600

And, the no. of ways in which the four digits can be chosen from available nine other digits = 9P2=72

Now, The no. of passwords possible are = 600 * 72 = 43200

GOOD LUCK

Answer 8

not permutations, as you are allowed repetition

Answer 9

right - i realized that after my first post

Answer 10

@satellite - isn't it 9*9*9*9 ?

Answer 11

yeah i forgot a 9

Answer 12

\[25\times 25\times 9\times 9\times 9\times 9\] more succinctly written as \(25^2\times 9^4\)