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Question

There are 8 events that can be scheduled in a week, then total number of ways that these 8 events are scheduled on exactly 6 days of a week is given by 266×k! where kN, then k is 
  1. 5
  2. 6
  3. 7
  4. 8


Solution

The correct option is C 7
Since, there are 8 events to be scheduled in 6 days.
This can be done in two ways.

Case I:
3 events are scheduled on one of the day and rest each day has 1 event each.
3 events out of 8 events can be selected in number of ways = 8C3
Now, these events can be arranged in 6 days out of 7 days of week in number of ways  = 7P6
Number of ways =8!5!×3!×7!=56×7!

Case II:
2 events are scheduled on couple of the days and rest each day has 1 event each.
Pair of 2 events out of 8 events can be selected in number of ways =8!4!×2!×2!×2!
Now, these events can be arranged in 6 days out of 7 days of week in number of ways  = 7P6
Number of ways =8!4!×2!×2!×2!×7!

Therefore, total number of ways =266×7!
k=7

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