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02 Nov 2021, 08:15
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C
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Question Stats:
70% (01:24) correct
30%
(01:34)
wrong
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A certain musical piece is to be played by an equal number of violinists and cellists. If there are 6 violinists and 2 cellists available to play the piece, how many different groups of musicians could be selected to play the piece?
(A) 12
(B) 15
(C) 27
(D) 28
(E) 70
(A) 12
(B) 15
(C) 27
(D) 28
(E) 70
02 Nov 2021, 10:55
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IMO C
If there are 6 violinists and 2 cellists, then for us to have an equal number of members in the troupe, we need either 2 violinists and 2 cellists OR 1 violinist and 1 cellist
First, we calculate the combinations for a 4 person team of 2 cellists and 2 violinists. To do so, we need to determine the number of ways to select 2 violinists from 6 (which gives 15) and 2 cellists from 2 (which is 1). This gives us 15 ways (15 times 1) for a 4 person group with 2 types of musicians each.
Second, we need to calculate the combinations for a 2 person team of 1 cellist and 1 violinist. We will repeat the process above. 1 violinist from 6 gives us 6 ways and 1 cellist from 2 gives us 2 ways. This gives our second scenario 12 possible ways (6 times 2) for a 2 person group with 1 type of musician each.
Since we could only have one (a 2 person squad) or the other (a 4 person squad), this is an "OR" probability which means that we add the 15 derived earlier from the first scenario (2V 2C) and 12 from the second scenario (1V 1C). This gives 27
If there are 6 violinists and 2 cellists, then for us to have an equal number of members in the troupe, we need either 2 violinists and 2 cellists OR 1 violinist and 1 cellist
First, we calculate the combinations for a 4 person team of 2 cellists and 2 violinists. To do so, we need to determine the number of ways to select 2 violinists from 6 (which gives 15) and 2 cellists from 2 (which is 1). This gives us 15 ways (15 times 1) for a 4 person group with 2 types of musicians each.
Second, we need to calculate the combinations for a 2 person team of 1 cellist and 1 violinist. We will repeat the process above. 1 violinist from 6 gives us 6 ways and 1 cellist from 2 gives us 2 ways. This gives our second scenario 12 possible ways (6 times 2) for a 2 person group with 1 type of musician each.
Since we could only have one (a 2 person squad) or the other (a 4 person squad), this is an "OR" probability which means that we add the 15 derived earlier from the first scenario (2V 2C) and 12 from the second scenario (1V 1C). This gives 27
26 Jul 2024, 20:26
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Given - A certain musical piece is to be played by an equal number of violinists and cellists.
To find - If there are 6 violinists and 2 cellists available to play the piece, how many different groups of musicians could be selected to play the piece?
The types of groups can be formed are based on who has min number of instruments/musicians in this case 2 cellists
so groups can form is either with 1 cellists or 2 cellists.
1. with 1 cellists.
6C1 * 2C1 = 6*2 = 12
2. with 2 cellists.
6C2 * 2C2 = 15
Total = 12+15 = 27.
Answer is C
To find - If there are 6 violinists and 2 cellists available to play the piece, how many different groups of musicians could be selected to play the piece?
The types of groups can be formed are based on who has min number of instruments/musicians in this case 2 cellists
so groups can form is either with 1 cellists or 2 cellists.
1. with 1 cellists.
6C1 * 2C1 = 6*2 = 12
2. with 2 cellists.
6C2 * 2C2 = 15
Total = 12+15 = 27.
Answer is C
