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25 Feb 2022, 03:15
Kudos
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (02:11) correct
37%
(02:21)
wrong
based on 363
sessions
History
Date
Time
Result
Not Attempted Yet
A promoter is organizing an opera concert. Ten singers are available for the program: 3 sopranos, 3 mezzos, 2 tenors and 2 baritones. If the promoter intends every segment to be a duet by performers with different vocal ranges, how many pairings of performers are possible?
A. 6
B. 10
C. 24
D. 36
E. 37
Are You Up For the Challenge: 700 Level Questions
A. 6
B. 10
C. 24
D. 36
E. 37
Are You Up For the Challenge: 700 Level Questions
25 Feb 2022, 22:20
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Bunuel
A quick way would be to find all the ways and subtract the opposite of what we intend to find.
Total ways = (3+3+2+2)C2 = 10C2 = 45
Ways when both the singers are from same group = 3C2+3C2+2C2+2C2 = 3+3+1+1 = 8
Answer = 45-8 = 37
E
General Discussion
25 Feb 2022, 22:35
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s m t b
3 3 2 2
s and m: 3 * 3 = 9
s and t: 3 * 2 = 6
s and b: 3 * 2 = 6
m and t: 3 * 2 = 6
m and b: 3 * 2 = 6
t and b: 2 * 2 = 4
Total=9 + 6 * 4 + 4 = 37 E)
3 3 2 2
s and m: 3 * 3 = 9
s and t: 3 * 2 = 6
s and b: 3 * 2 = 6
m and t: 3 * 2 = 6
m and b: 3 * 2 = 6
t and b: 2 * 2 = 4
Total=9 + 6 * 4 + 4 = 37 E)
