Question

the access code for a car's security system consists of four digits. the first digit cannot be 1 and the last digit must be even or zero. how many different codes are available?

Answer 1

1st value: 1 in 9
2nd value: 1 in 10
3rd value 1 in 10
4th value: 1 in 5
\[9*10*10*5=?\]

Answer 2

thanks so much shane. that looks right!

Answer 3

yw :)

Answer 4

here's one more i can't seem to figure out, if you're willing.
A certain lottery has 30 numbers. In how many different ways can 6 of the numbers be selected? Assume that order of selection is not important.

Answer 5

Can each number be selected more than once?

Answer 6

the question does not say. i typed it word for word...

Answer 7

My assumption is that each number can only be selected once...since it's a lottery

Answer 8

i don't think they can be selected more than once because it said 6 numbers, so think your assumption is correct.

Answer 9

I'm no probability expert but I believe it would simply be:
\[30*29*28*27*26*25=?\]

Answer 10

that looks to be 427,518,000. the answer is supposed to be 593,775. can't figure out how they got that answer.

Answer 11

I guess since the order doesn't matter it would be:
\[\frac{n!}{r!(n-r)!}=\frac{30!}{6!(30-6)!}\]

Answer 12

Which = 593,775

Answer 13

but how do you figure that exactly. i have a calculator with the x! function, but the number i get does not resemble this, so i must be doing something wrong.

Answer 14

I'm not sure how to do it on my calculator either (TI-84). I just used Microsoft Math to check it. It's worth the download and it's free.

http://www.microsoft.com/en-us/download/details.aspx?id=15702

Answer 15

ok i'll try it - thanks a million.

Answer 16

np :)

Answer 17

ok. i downloaded the calculator. handy little thing. but i still can't figure out what to input to get this answer. i typed in {30!}{6!(30-6)!} i got back some long decimal answer. any suggestions?

Answer 18

You're missing the division sign :)