Question

a student loan administrator distributes pin numbers to its debtors. each pin consists of 2 letters followed by 3 numbers. (assume repetition is allowed and order is important)
a) how many different pins are there?
b) what is the probability a pin number selected at random ends in 000?
c) what is the probability a pin number selected at random begins with AA?
d) what is the probability a pin number selected at random begins with A and ends with 00?
e) what is the probability a pin number selected at random has a repeated letter and different numbers?

Answer 1

\[\26\times 26\times 10\times 10\times 10=26^2\times 1000\] for the first one

Answer 2

b) ends is 000
\[26 \times 26\]

Answer 3

i guess we should compute
\[26^2=676\] so first answer is
a) 676000
b)676

Answer 4

oh i am sorry i should learn to read. says "what is the probability it ends in 000"!
answer is
\[\frac{676}{676000}=\frac{1}{1000}\]

Answer 5

c) begins with AA \[\frac{1000}{676000}=\frac{1}{676}\]

Answer 6

for b why would it only be 26 * 26?

Answer 7

because you know that the last 3 digits are 000 yes? there is only once choice here. you have 26 choices for first letter, 26 choices for second letter, but no choices for the three numbers.

Answer 8

ohhhh okay! and where did the 1000 come from for c?

Answer 9

in c you are given the first and second letter as AA
so you have no choices for letters, only choices for numbers.
they all look like AA _ _ _

Answer 10

so your only choices are in the three numbers that follow. 10 for the first number, 10 for the second and 10 for the third. so by counting principle you have 10*10*10 = 10^3= 1000 ways to do this

Answer 11

ohhhh okay!

Answer 12

so lets do d slowly

Answer 13

okay

Answer 14

begins with A
ends with 00 so it looks like
A (some letter) (some number) 0 0

Answer 15

only choices are second letter and first number. the rest is fixed. number of choice is 26 for the letter times 10 for the number. number of possibilities is 26*10 = 260

Answer 16

that of course is not the answer to the question. that is the answer to "how many"
the answer to the probability question is
\[\frac{26\times 10}{676000}\]

Answer 17

reduce to get
\[\frac{1}{2600}\]

Answer 18

last one is hardest. let me know when you are ready for that one

Answer 19

i'm ready!!!!

Answer 20

ok first to letters are the same. so it is clear that for the first two there are 26 possibilities?
AA, BB, CC, ..., XX, YY, ZZ

Answer 21

that should be ok. i hope. now the numbers are a bit trickier. they all have to be different. at least i assume that is what "different numbers" means. you have three numbers to put in the slots
__ __ __
for the first one you have 10 choices , but now you have only 9 choices for the second because you cannot repeat the first one. then for the third you have 8 choices because you cannot repeat the first or second. so number of possibilities total is
\[26\times 10\times 9\times 8\]

Answer 22

and your "final answer" is
\[\frac{26\times 10\times 9\times 8}{676000}=\frac{9}{325}\]

Answer 23

would it not be 26^2 since their double?