In how many ways 6 Europeans, 5 Indians and 9 Chinese be seated in a row, so that all person of same nationality sits together.
Question
In how many ways can 6 Europeans, 5 Indians, and 9 Chinese be seated in a row, so that all persons of same nationality sit together?
Solution
To solve this problem, we need to use the concept of permutations in combinatorics. Here are the steps:
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First, consider each group of people of the same nationality as a single entity. So, we have 3 entities: Europeans, Indians, and Chinese.
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These 3 entities can be arranged in a row in 3! (factorial) ways, which is 321 = 6 ways.
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Within each entity, the individuals can also be arranged among themselves. The 6 Europeans can be arranged in 6! ways, the 5 Indians in 5! ways, and the 9 Chinese in 9! ways.
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Therefore, the total number of ways in which 6 Europeans, 5 Indians, and 9 Chinese can be seated in a row, so that all persons of the same nationality sit together, is 3! * 6! * 5! * 9!.
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Calculate the factorial values and multiply them to get the final answer.
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