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# help me out with this one

• 09-11-2010 9:27pm
Registered Users Posts: 5,325 ✭✭✭

Right.. You have to crack the code.. how many different combination can there be ... You have a 3 Pin code in the form of a deck of cards.

Now you know the numbers but not the suit

So you know the code has a 3 a 10 and a Jack but you don't know what suit they are.

So the code will be something like 3hearts / 10 clubs / Jack hearts etc

How many different combination can there be ?

• Registered Users Posts: 2,294 ✭✭✭

384
at a guess.

• Registered Users Posts: 5,325 ✭✭✭

thee glitz wrote: »
384
at a guess.

How did you get to this number ?

• Registered Users Posts: 2,294 ✭✭✭

NeVeR wrote: »
How did you get to this number ?
You've 12 cards, the 3 cards * 4 suits.
The 1st card can be any of the 12. Say it's a Jack.
The 2nd has to be a 3 or 10, so you've 8 choices.
If the 2nd is a 10, the 3rd has to be one of the 3's.
So 12*8*4 = 384.

• Registered Users Posts: 3,360 ✭✭✭

Hmmm not sure about that one

He says "the code has a 3 a 10 and a JacK"
The 3 10 and Jack can be arranged in 6 different ways.
They can be one of four suits so you've 12 options for each arrangement
So I'm guessing there's 144 different combinations??

• Registered Users Posts: 2,294 ✭✭✭

GaryCocs wrote: »
Hmmm not sure about that one

He says "the code has a 3 a 10 and a JacK"
The 3 10 and Jack can be arranged in 6 different ways.
They can be one of four suits so you've 12 options for each arrangement
So I'm guessing there's 144 different combinations??
Take one of the 6 ways of arranging the eg 3,10,J
There are 64 ways of arranging the suits (4^3)
4^3 = 64, *6 ways = 384

• Registered Users Posts: 3,360 ✭✭✭

Ya forgot that you can use the same suit 3 times so

4 * 4 * 4

4 * 3 * 2

whoops!!

• Closed Accounts Posts: 17,919 ✭✭✭✭

The first card means

3 cards of 4 different suits = 12 possible outcomes

The second card drawn will leave

2 cards of 4 different suits = 8 possible outcomes

The last draw will only leave

1 card of four different suits = 4 outcomes

Therefore this leaves us with the simple multiplication 12*8*4 = 384