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01 Mar 2026, 07:34
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
58% (02:50) correct
42%
(02:43)
wrong
based on 45
sessions
History
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Time
Result
Not Attempted Yet
A hiring manager will conduct six interviews during one afternoon and will also take two coffee breaks.
The eight time slots may be arranged in any order, subject to the following conditions:
• There must be at least two interviews scheduled between the two coffee breaks.
• Neither coffee break may be scheduled in the first or last time slot.
In how many different ways can the manager arrange the eight time slots?
A. 3 * 6!
B. 6 * 6!
C. 10 * 6!
D. 15 * 6!
E. 21 * 6!
The eight time slots may be arranged in any order, subject to the following conditions:
• There must be at least two interviews scheduled between the two coffee breaks.
• Neither coffee break may be scheduled in the first or last time slot.
In how many different ways can the manager arrange the eight time slots?
A. 3 * 6!
B. 6 * 6!
C. 10 * 6!
D. 15 * 6!
E. 21 * 6!
01 Mar 2026, 12:52
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kevincan
Let's assume there are \(8\) time slots as shown below -
\(s_1 \quad s_2 \quad s_3 \quad s_4 \quad s_5 \quad s_6 \quad s_7 \quad s_8\)
The coffee break cannot be set in either slot \(s_1\) or \(s_8\), so one has to choose two slots between \(s_2\) and \(s_7\), both inclusive.
Number of ways in which two slots can be selected from six available slots = \(^6C_2\) ways = 15 ways
Among these 15 ways exists slots which are consecutive , such \(s_2\) and \(s_3\), \(s_3\) and \(s_4\) so on, and combinations, of breaks which are separated by only one interview, for example \(s_2\) and \(s_4\), \(s_3\) and \(s_5\) so on. We have to exclude them.
Number of consecutive slots = 5 (\(s_2\) & \(s_3\); \(s_3\) & \(s_4\); \(s_4\) & \(s_5\); \(s_5\) & \(s_6\); \(s_6\) & \(s_7\))
Number of slots separated by only one interview slot = 4 (\(s_2\) & \(s_4\); \(s_3\) & \(s_5\); \(s_4\) & \(s_6\); \(s_5\) & \(s_7\))
Remaining = 15 - 5 - 4 = 6
Therefore there are only 6 ways in which the coffee breaks can be arranged, and we will end up consuming two slots for that. The remaining 6 slots can be used for interview, and in these six slots the six interviews can be arranged in 6! ways.
Total = 6 * 6!
Option B
01 Mar 2026, 13:04
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Explained in great detail! Thanks for taking the time to write all this
