The number of ways can 3 engineers and 4 nurses be seated on a bench with the engineers seated together is
Question
The number of ways can 3 engineers and 4 nurses be seated on a bench with the engineers seated together is
Solution
To solve this problem, we can use the concept of permutations in combinatorics. Here are the steps:
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Consider the 3 engineers as a single entity since they have to sit together. So, we now have 2 entities (the engineers as a group and the 4 nurses) to arrange.
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These 2 entities can be arranged in 5! (5 factorial) ways, which is 54321 = 120 ways.
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However, within the group of engineers, they can arrange themselves in 3! (3 factorial) ways, which is 321 = 6 ways.
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Therefore, the total number of ways the engineers and nurses can be seated with the engineers together is 5! * 3! = 120 * 6 = 720 ways.
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