Question:
Six boys and six girls sit in a row at random . find the probability that the boys and girls sit alternatively.
Answer:
Given, 6 boys and 6 girls sit in a row at random.
Then, the total number of arrangement of 6 boys and 6 girls = arrangement of 12 persons = 12!
Now, boys and girls sit alternatively.
So, the total number of arrangement = 2* 6! * 6!
Now, P(boys and girls sit alternatively) = (2* 6! * 6!)/12!
= (2* 6 * 5! * 6!)/(12 * 11!)
= (5! * 6!)/11!
= (5 * 4 * 3 * 2 * 1 * 6!)/(11 * 10 * 9 * 8 * 7 * 6!)
= (5 * 4 * 3 * 2)/(11 * 10 * 9 * 8 * 7)
= (4 * 3)/(11 * 9 * 8 * 7)
= 3/(11 * 9 * 2 * 7)
= 1/(11 * 3 * 2 * 7)
= 1/462
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