9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
A)23
B)30
C)42
D)60
E)126
OAD
Basket ball players
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Hi j_shreyans,
This question does NOT ask us to put players "in order", it asks us for groups of players. That clue points to using the Combination Formula. This question has 2 types of players though (guards and forwards), so we have to use the Combination Formula twice (once for each type of player), then multiply the results.
Guards:
There are 6 guards and we're asked for sets of 3.
6c3 = 6!/(3!3!) = 6(5)(4)(3)(2)(1)/3(2)(1)(3)(2)(1) = 20 different sets of 3 guards
Forwards:
There are 3 forwards and we're asked for groups of 2.
3c2 = 3!/(2!1!) = 3(2)(1)/(2)(1)(1) = 3 different groups of 2 forwards
(20)(3) = 60 possible teams
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
This question does NOT ask us to put players "in order", it asks us for groups of players. That clue points to using the Combination Formula. This question has 2 types of players though (guards and forwards), so we have to use the Combination Formula twice (once for each type of player), then multiply the results.
Guards:
There are 6 guards and we're asked for sets of 3.
6c3 = 6!/(3!3!) = 6(5)(4)(3)(2)(1)/3(2)(1)(3)(2)(1) = 20 different sets of 3 guards
Forwards:
There are 3 forwards and we're asked for groups of 2.
3c2 = 3!/(2!1!) = 3(2)(1)/(2)(1)(1) = 3 different groups of 2 forwards
(20)(3) = 60 possible teams
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
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Take the task of creating a team and break it into stages.j_shreyans wrote:9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
A)23
B)30
C)42
D)60
E)126
Stage 1: Select 3 guards from the 6 eligible guards
Since the order in which we select the guards does not matter, we can use combinations.
We can select 3 guards from the 6 eligible guards in 6C3 ways (= 20 ways)
So, we can complete stage 1 in 20 ways
If anyone is interested, we have a free video on calculating combinations (like 6C3) in your head: https://www.gmatprepnow.com/module/gmat-counting?id=789
Stage 2: Select 2 forwards from the 3 eligible forwards
Since the order in which we select the forwards does not matter, we can use combinations.
We can select 2 forwards from the 3 eligible forwards in 3C2 ways (= 3 ways)
So, we can complete stage 2 in 3 ways
By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus create a basketball team) in (20)(3) ways ([spoiler]= 60 ways[/spoiler])
Answer: D
--------------------------
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Brent
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No. of ways to select 3 Guards out of 6 guards = 6C3 = 20j_shreyans wrote:9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
A)23
B)30
C)42
D)60
E)126
OAD
No. of ways to select 2 forwards out of 3 forwards = 3C2 = 3
Total possible ways = 20 x 3 = 60
Answer: Option D
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The guards can be chosen in the following number of ways:j_shreyans wrote:9 basketball players are trying out to be on a newly formed basketball team. Of these players, 5 will be chosen for the team. If 6 of the players are guards and 3 of the players are forwards, how many different teams of 3 guards and 2 forwards can be chosen?
A)23
B)30
C)42
D)60
E)126
6C3 = 6!/[(3!(6 - 3)!] = 6!/)3!3!) = (6 x 5 x 4)/3! = (6 x 5 x 4)/(3 x 2 x 1) = 20 ways
The forwards can be selected in the following number of ways:
3C2 = (3 x 2)/2! = 3 ways
We can pair up each of the 20 ways of choosing guards with each of the 3 ways of choosing forwards. So the total number of teams of 3 guards and 2 forwards is 20 x 3 = 60.
Answer: D
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