Question
In a board meeting, 8 delegates from number 1 to 8 are sitting around a circular table. Number 4 and 5 always sit together and number 1 always sits next to number 4. If number 8 always sits exactly opposite number 3, in how many ways can the seating be done?
Answer: Option C
:
C
Let's fix number 8 at a slot at the table, automatically, number 3 also gets fixed. Out of the remaining 6 delegates, 4 and 5 will be together and can be arranged in 2! Ways amongst each other. Also for each of these ways, number 1 can sit next to 4 in only one way.
Now 1,4,5 can be placed only in 2 ways(See below).
This question now becomes the arrangement of the remaining 3 people × 4= 3! × 4. Option (c)
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:
C
Let's fix number 8 at a slot at the table, automatically, number 3 also gets fixed. Out of the remaining 6 delegates, 4 and 5 will be together and can be arranged in 2! Ways amongst each other. Also for each of these ways, number 1 can sit next to 4 in only one way.
Now 1,4,5 can be placed only in 2 ways(See below).
This question now becomes the arrangement of the remaining 3 people × 4= 3! × 4. Option (c)
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