Permutations And Combinations

Question
CBSEENMA11014098

Find the value of n such that:

straight P presuperscript straight n subscript 5 space equals space 42 straight P presuperscript straight n subscript 3 comma space straight n greater than 4

Solution

straight P presuperscript straight n subscript 5 space equals space 42 straight P presuperscript straight n subscript 3 comma space straight n greater than 4
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#6 {main}</pre>

 
rightwards double arrow         fraction numerator 1 over denominator left parenthesis straight n minus 5 right parenthesis factorial end fraction space equals space 42. space fraction numerator 1 over denominator left parenthesis straight n minus 3 right parenthesis factorial end fraction

rightwards double arrow         fraction numerator 1 over denominator left parenthesis straight n minus 5 right parenthesis factorial end fraction space equals space 42. space fraction numerator 1 over denominator left parenthesis straight n minus 3 right parenthesis space left parenthesis straight n minus 4 right parenthesis space left parenthesis straight n minus 5 right parenthesis factorial end fraction
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#2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs()
#3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...')
#4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array)
#5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array)
#6 {main}</pre>
rightwards double arrow           straight n squared minus 7 straight n plus 12 equals 42

rightwards double arrow            straight n squared minus 7 straight n minus 30 space equals 0
rightwards double arrow           (n - 10) (n + 3) = 0
rightwards double arrow                         n = 10                                 [∵ space space space straight n equals negative 3 not an element of straight N]
Hence,       n = 10

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Some More Questions From Permutations and Combinations Chapter

Determine K, so that K + 2, 4K – 6 and 3K – 2 are three consecutive terms of an A.P.