Sitting Side-by-side
male students and female students sit around a round table. If the probability of all three female students sitting side-by-side is what is the value of
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1 solution
Event that the three females will sit side-by-side / All event = 1 / a
Circular Permutation:
(n-1)! = (10-1)! = 362,880
This is the total number of possible arrangements.
Now, to solve for the total number of possible arrangements under the condition that the three females will sit side-by-side:
*Consider the three females as one since they will sit together for all the arrangements under the said condition.
So:
7 males + 1 group of females = 8 people
Circular Permutation:
(n-1)! = (8-1)! = 5040
*Though the three females will sit side-by-side, they can also change their arrangement in the group.
So:
Permutation of all objects taken all at a time:
n! = 3! = 6
(5,040)(6) / 362,880 = 1 / a
Final Answer: a = 12