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Can someone please help me solve the following problem?

In the absence of the chairman, a committee of three vice-chairmen and four ordinary members is to sit on a platform. In how many ways can they be arranged if one of the vice-chairmen sits in the middle?

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    What have you tried so far? Are the vice-chairmen only distinghuishable as vice-chairmen? Same question for the ordinary members. – 2017-02-28
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    @drhab: since they are humans they a likely to be unique – 2017-03-01

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First figure out how many ways you can fill that middle seat. After that, figure out how many ways there are to fill the remaining 6 seats (think how many ways to fill the first, then the second,...up to the 6th seat). Multiply those numbers together using the multiplication principle of counting. If you're not familiar with that principle, you'd best try to learn it.

I suggest you try to do the problem yourself before looking at the answer below:

There are 3 ways to fill the first seat. For each of these three ways, there are 6! or 720 ways to fill the remaining 6 seats. Multiplying 3 and 720 gives the final total of 2160 possible seatings.