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Compute:

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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32.

Compute:

$fraction numerator 6 factorial over denominator 3 factorial end fraction$

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33.

Compute:

$fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 1 over denominator 7 factorial end fraction space$

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34.

Compute:

$fraction numerator straight n factorial over denominator left parenthesis straight n minus 2 right parenthesis factorial end fraction$

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35.

Find x, if $fraction numerator 1 over denominator 6 factorial end fraction plus fraction numerator 1 over denominator 7 factorial end fraction equals fraction numerator straight x over denominator 8 factorial end fraction$

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Long Answer Type

36.

Evaluate: $fraction numerator straight n factorial over denominator straight r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction comma$ when

(a) n = 6, r = 2, (b) n = 6, r = 4, (c) n = 9, r = 4

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37.
Evaluate: $fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction comma$ when:

(a) n = 6, r = 2, (b) n = 7, r = 7, (c) n = 9, r = 0

(a) n = 6, r = 2

$rightwards double arrow$ $fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction equals fraction numerator 6 factorial over denominator 4 factorial end fraction equals fraction numerator 6 cross times 5 cross times 4 factorial over denominator 4 factorial end fraction space equals space 6 cross times 5 space equals 30$

(b) n = 7, r = 7

$rightwards double arrow$ $fraction numerator straight n factorial over denominator left parenthesis straight n minus straight r right parenthesis factorial end fraction space equals space fraction numerator 7 factorial over denominator 0 factorial end fraction space equals space 7 factorial space equals space 7 cross times 6 cross times 5 cross times 4 cross times 3 cross times 2 cross times 1 space equals space 5040$ (∵ 0! = 1)

(c) n = 9, r = 0

$rightwards double arrow$ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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38.

Evaluate: $fraction numerator straight n factorial over denominator r factorial space left parenthesis straight n minus straight r right parenthesis factorial end fraction comma$ when:

(a) n = 9, r = 0, (b) n = 8, r = 1, (c) n = 9, r = 9

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Short Answer Type

39.

If (n+1)! = 30 (n - 1)!, find value of n.

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40.

If $fraction numerator straight n factorial over denominator 2 factorial space left parenthesis straight n minus 2 right parenthesis factorial end fraction colon space fraction numerator straight n factorial over denominator 4 factorial space left parenthesis straight n minus 4 right parenthesis factorial end fraction equals space 2 space colon space 1$

Find value of n.