license plates / playing cards / standard dice

[xjinaloveskangin]

1) How many different license plates could be made that contain 2 letters followed by 3 digits (0 to 9)

2) Out of a standard deck of cards, what is the probability of selecting three consecutive clubs?

3) On a standard 6-sided die, what is the probability of rolling 2 or a 3 four times in a row?

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I find these probability questions realy confusing. I'm very confused on how to solve the first one, and I think the answr for the second question is 13/52 which is 25% but I'm not sure. Also, on the third on, I'm not sure what to do either.

Please help asap. Thank you very much!

 

[Goistein]

How many charactars does a licence plate have?

2.
(13/52)(12/51)(11/50). Justmultiply the chances of getting a club.

3.
Does this mean 2,2,2,2, or can it be 2,3,3,2?

 

[xjinaloveskangin]

^hmm im not sure.

 

[pka]

3. Does this mean 2,2,2,2, or can it be 2,3,3,2?

Lets do it both ways:
2222 or 3333 \(\displaystyle \L 2\left( {\frac{1}{6}} \right)^4 .\)

2323: Either a 2 or a 3 on any of four throws.
\(\displaystyle \L \left( {\frac{1}{3}} \right)^4\)

 

[xjinaloveskangin]

ooh thank you so much!


btw, can someone help me on the first problem too?? thank you

 

[pka]

1) How many different license plates could be made that contain 2 letters followed by 3 digits (0 to 9)

\(\displaystyle \L \left( {26} \right)^2 \left( {10} \right)^3 .\)

 

[xjinaloveskangin]

^so would you just multiply those two numbers?