# A man invites 10 friends to a party and places 5 at one table and 5 at another table, the tables being round. The number of ways in which he can arrange the friends?

$Number\;of\;ways\;selecting\;5\;out\;of\;10\;is\;_{}^{10}\textrm{C}_5\\* and\;arranging\;them\;in\;circular\;table\;then\;number\;of\;arrangement\;of\\*5\;persons\;in\;circualr\;table\;is\;(5-1)!\\* \therefore\;required\;number\;of\;ways=_{}^{10}\textrm{C}_5\times (4!)^2$

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