Permutation and Combinations (Separation)

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Eight students are to be arranged in a row. Find the number of ways to arrange them if three particular students must be separated.

1

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5
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Hint:First we arrange five students excluding the three that should be separated. Then what we should do is put the rest of the 3 in the gaps of the five student. There are altogether 6 places to arrange these 3 (4 gaps and the 2 corners). So from the first part we have 5! and the second part for which 3 must be arranged can you make a guess?