# Number of Possible 3-Card Hands with and without Order Consideration

• r-soy
In summary, there are 756 possible hands when order is taken into consideration and 4536 possible hands when order is not taken into consideration. However, the correct answers are 324 and 648 respectively. This is because combinations should be used when order is not important, while permutations should be used when order is important.
r-soy
Q : Suppose 9 cards are number with the 9 digits from 1 to 9 . A 3-card hand is dealt, 1 card at a time . How many hands are possible where :

1 ) Order is taken into consideration ?

2 ) order is not taken into considreation ?

----------Ansewr >>

1 - 9C3 X 9C1 = 84 X 9 = 756

2 - 9P3 X 9P1 = 504 X 9 = 4536

You have C and P backwards. Combinations is when you don't care about the order; permutations is when you do. "123" and "321" are the same combination, but they are two possible permutations of 1, 2, and 3.

r-soy said:
Q : Suppose 9 cards are number with the 9 digits from 1 to 9 . A 3-card hand is dealt, 1 card at a time . How many hands are possible where :

1 ) Order is taken into consideration ?

2 ) order is not taken into considreation ?

----------Ansewr >>

1 - 9C3 X 9C1 = 84 X 9 = 756

2 - 9P3 X 9P1 = 504 X 9 = 4536

r-soy said:

The ansewr now correct ?

1 - 9P3 X 9P1 = 504 X 9 = 4536

2 - 9C3 X 9C1 = 84 X 9 = 756

No, they are not.

Help me Give me the answer

No .

I tay agine

1 - 9C2 X 9C1 = 36 X 9 = 324

2 - 9P2 X 9P1 = 72 X 9 = 648

I can't try more thanks all

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