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If $straight C presuperscript straight n subscript 8 space equals space straight C presuperscript straight n subscript 2 comma$ find $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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162.

If $space space straight C presuperscript 10 subscript straight r space equals space straight C presuperscript 10 subscript 2 comma$ find the values of r.

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163.

Determine n if:

$straight C presuperscript 2 straight n end presuperscript subscript 3 colon straight C presuperscript straight n subscript 3 space equals space 12 colon 1$

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164. Determine n if:

straight C presuperscript 2 straight n end presuperscript subscript 3 space colon space straight C presuperscript straight n subscript 3 space equals space 11 colon 1

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165. In how many ways can a team of 3 boys and 3 girls be selected out of 5 boys and 4 girls?

Number of boys = 5
Number of boys to be selected = 3

$rightwards double arrow$ Number of combinations (selections) = $straight C presuperscript straight n subscript straight r space equals space straight C presuperscript 5 subscript 3 space equals space fraction numerator 5 factorial over denominator 3 factorial space 2 factorial space end fraction space equals space 10$ ...(i)
Number of girls = 4
Number of girls to be selected = 3

$rightwards double arrow$ Number of selections = $straight C presuperscript straight n subscript straight r space equals space straight C presuperscript 4 subscript 3 space equals space fraction numerator 4 factorial over denominator 3 factorial space 1 factorial end fraction equals 4$ ...(ii)
∴ From (i) and (ii), by fundamental principle of counting, the number of selections
= 10 x 4 = 40
Hence, the number of ways in which 3 boys and 3 girls out of 5 boys and 4 girls can be selected = 40

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166. A bag contains 5 different black balls and 6 different red balls. Determine the number of ways in which 2 black and 3 red balls can be selected?

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167.

In how many ways can a student choose a programme of 5 courses if 9 courses are available and 2 specific courses are compulsory for every student?

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168. The English alphabet has 5 vowels and 21 consonants. How many words with two different vowels and 2 different consonants can be formed from the alphabet?

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