Find the value of n such that: from Mathematics Permutations an
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    Permutations and Combinations

    Multiple Choice QuestionsShort Answer Type

    61.

    Find the value of:

    fraction numerator left parenthesis straight n plus 3 right parenthesis factorial over denominator left parenthesis straight n plus 1 right parenthesis factorial end fraction



    92 Views
    Answer
    62.

    Convert the following to factorial notation;

    (a) <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #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>   (b) 5 times 6 times 7 times 8 times 9 times 10 times 11 times 12

    91 Views
    Answer
    63.

    Show that (n - 1)! + n! = [n+1] x (n - 1)!

    100 Views
    Answer
    64.

    Find the largest value of n so that 2n divides 16!

    105 Views
    Answer
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    65.

    Prove that 33! is divisible by <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #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> What is the largest value of n so that 33! is divisible byspace space space 2 to the power of straight n?

    101 Views
    Answer
    66.

    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

    84 Views
    Answer
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    67.

    Find the value of n such that:

    space space fraction numerator straight P presuperscript straight n subscript 4 over denominator straight P presuperscript straight n minus 1 end presuperscript subscript 4 end fraction equals 5 over 3 comma space straight n greater than 4


    space space space space straight P presuperscript straight n subscript 4 divided by straight P presuperscript straight n minus 1 end presuperscript subscript 4 space equals space 5 divided by 3

    rightwards double arrow         bevelled fraction numerator space space space fraction numerator straight n factorial over denominator left parenthesis straight n minus 4 right parenthesis factorial end fraction over denominator begin display style fraction numerator left parenthesis straight n minus 1 right parenthesis factorial over denominator left parenthesis straight n minus 5 right parenthesis factorial end fraction equals space 5 divided by 3 end style end fraction

    rightwards double arrow          fraction numerator straight n factorial over denominator left parenthesis straight n minus 4 right parenthesis factorial end fraction cross times fraction numerator left parenthesis straight n minus 5 right parenthesis factorial over denominator left parenthesis straight n minus 1 right parenthesis factorial end fraction equals 5 over 3

    rightwards double arrow            space space space fraction numerator straight n left parenthesis straight n minus 1 right parenthesis factorial over denominator left parenthesis straight n minus 4 right parenthesis left parenthesis straight n minus 5 right parenthesis factorial end fraction cross times fraction numerator left parenthesis straight n minus 5 right parenthesis factorial over denominator left parenthesis straight n minus 1 right parenthesis factorial end fraction equals 5 over 3

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    rightwards double arrow                             5n - 20 = 3n

    rightwards double arrow                    2n = 20 or n = 10.

    86 Views
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    68.

    Find r, if

    space straight P presuperscript 5 subscript straight r space equals space 2. straight P presuperscript 6 subscript straight r minus 1 end subscript

    121 Views
    Answer
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    69.

    Find r, if

      <pre>uncaught exception: <b>mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied</b><br /><br />in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56<br />#0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #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>

    95 Views
    Answer
    70.

    Find r, if 

    space space space space 5. space straight P presuperscript 4 subscript straight r space equals space 6. space straight P presuperscript 5 subscript straight r minus 1 end subscript

    71 Views
    Answer
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