James has 5 baseball cards, 3 football cards, and 1 hockey card (all different). He picks 2 cards at random without replacement. How many possible outcomes (card combinations) are there?
72
9
81
15
*i think theirs 72 but not sure
You can also do 3x5x1 or any way because you will get the same answer.
no
The order in which the cards are drawn should not matter.
They even used the word "combination", which implies that the order does not matter.
So you are simply choosing 2 of the 9 cards
= C(9,2)
= 9!/(2!7!)
= 36
The answer of 72 would be correct if the order in the card does matter.
But suppose you draw one of the baseball cards and the hockey card,
or you draw the hockey card, then the same baseball card.
Would you not have the same combination??
None of the given answers are correct.
wtf lol
Multiply 5 and 3 and the answer to that multiply by 1
Why did the baseball card go to the game?
Because it heard it was a big hit!
When James picks 2 cards at random without replacement, we can use the formula for combinations to find the number of possible outcomes. The formula for combinations is:
nCr = n! / (r!(n-r)!)
Where n is the total number of cards and r is the number of cards being picked.
In this case, n = 9 (5 + 3 + 1) and r = 2.
Plugging in the values, we get:
9C2 = 9! / (2!(9-2)!)
= 9! / (2! * 7!)
= (9 * 8 * 7!) / (2! * 7!)
= (9 * 8) / 2!
= 72 / 2
= 36
So, there are 36 possible outcomes or card combinations when James picks 2 cards at random without replacement. Therefore, the correct answer is 36, not 72.
To determine the number of possible outcomes for picking 2 cards at random without replacement from a set of 9 cards (5 baseball, 3 football, and 1 hockey), we can use the concept of combinations.
The number of combinations of picking r items from a set of n items is calculated using the formula:
nC(r) = n! / [(n-r)! * r!]
In this case, n = 9 (since there are 9 cards in total) and r = 2 (since we are picking 2 cards without replacement).
Plugging in the values into the formula, we get:
9C2 = (9!)/( (9-2)! * 2! )
= (9!)/(7! * 2!)
= (9 * 8 * 7!)/(7! * 2 * 1)
= 9 * 4
= 36
Therefore, there are 36 possible outcomes (card combinations) when James picks 2 cards at random without replacement from the given set of cards. Hence, the correct answer is not among the given options of 72, 9, 81, or 15.