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Difficulty:
45%
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69% (02:05) correct
31%
(02:11)
wrong
based on 136
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There are n members in a certain department, including Michael. Two representatives are to be selected to attend a company conference. If there are 55 possible combinations in which Michael is not selected, what is the value of n?
A. 11
B. 12
C. 15
D. 18
E. 22
A. 11
B. 12
C. 15
D. 18
E. 22
mbastudent007
Joined: 17 Jun 2022
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29 Jun 2022, 13:04
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Using combinations,
All possibilities = n C 2
Possibilities in which Michael is selected = 1C1 * (n-1)C1 = n - 1
Therefore possibilities in which Michael is not selected is the difference between these two
nC2 - (n-1)C1
[n (n-1) /2 ] - (n - 1)
n^2 - 3n - 108 = 0
n = 12 or -9
-9 not possible so n =12
Posted from my mobile device
All possibilities = n C 2
Possibilities in which Michael is selected = 1C1 * (n-1)C1 = n - 1
Therefore possibilities in which Michael is not selected is the difference between these two
nC2 - (n-1)C1
[n (n-1) /2 ] - (n - 1)
n^2 - 3n - 108 = 0
n = 12 or -9
-9 not possible so n =12
Posted from my mobile device
29 Jun 2022, 13:15
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Combination is when n > k the order doesn’t matter and there’s no repetition.
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