Nine person sit for a photograph in a row. Find the probability that a family of three always sit together
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Given:
Total number of people = 9
To find:
The probability that a family of three always sit together.
Solution:
The total possibility of arranging 9 people = 9!
Assume that the family of 3 is in a group and treat them as a single person, then the number of people becomes 7
Total possibility to arrange these seven people = 7!
We can arrange the family members within themselves, therefore the probability becomes 7! 3!
The required probability = 7! 3! / 9!
= 1/ 12
Therefore, the required probability is 1/12.
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