5 boys and 5 girls have to sit around a table. The number of ways in which all of them can sit so that no two boys and no two girls are together is
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For alternating arrangements in a circle (e.g., n men and n women), first arrange one group in \((n-1)!\) ways. Then, arrange the second group in the \(n\) spaces created, which can be done in \(n!\) ways. The total ways are \((n-1)! \times n!\).