{"id":6951,"date":"2021-10-22T01:57:56","date_gmt":"2021-10-21T20:27:56","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6951"},"modified":"2021-10-25T01:20:48","modified_gmt":"2021-10-24T19:50:48","slug":"the-number-of-ways-in-which-6-men-and-5-women-can-dine-at-a-round-table-if-no-two-women-are-to-sit-together-is-given-by","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-number-of-ways-in-which-6-men-and-5-women-can-dine-at-a-round-table-if-no-two-women-are-to-sit-together-is-given-by\/","title":{"rendered":"The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by"},"content":{"rendered":"

Solution :<\/h2>\n

The number of ways to n people on circular table is (n-1)!<\/p>\n

So, first we fix position of men, the number of ways to sit men = 5!<\/p>\n

Now, women can sit in the gaps between men, there are 6 gaps between 5 mens,<\/p>\n

So, women can sit in \\(^6P_5\\) ways<\/p>\n

Hence, total number of ways = 5! x \\(^6P_5\\) = 5! x 6!<\/p>\n

\n

Similar Questions<\/h3>\n

A student is to answer 10 out of 13 questions in an examination such that he must choose atleast 4 from the first five questions. The number of choices available to him is<\/a><\/p>\n

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How many ways are there to arrange the letters in the word \u2018GARDEN\u2019 with the vowels in alphabetical order ?<\/a><\/p>\n

If the letters of the word \u2018SACHIN\u2019 are arranged in all possible ways and these words are written out as in dictionary, then the word \u2018SACHIN\u2019 appears at serial number<\/a><\/p>\n

At an election, a voter may vote for any number of candidates not greater than the number of candidates to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for atleast 1 candidate, then the number of ways in which he can vote is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : The number of ways to n people on circular table is (n-1)! So, first we fix position of men, the number of ways to sit men = 5! Now, women can sit in the gaps between men, there are 6 gaps between 5 mens, So, women can sit in \\(^6P_5\\) ways Hence, total …<\/p>\n

The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,47],"tags":[],"yoast_head":"\nThe number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/the-number-of-ways-in-which-6-men-and-5-women-can-dine-at-a-round-table-if-no-two-women-are-to-sit-together-is-given-by\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The number of ways in which 6 men and 5 women can dine at a round table, if no two women are to sit together, is given by\" \/>\n<meta property=\"og:description\" content=\"Solution : The number of ways to n people on circular table is (n-1)! 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