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Permutations and Combinations

Short Answer Type

241. From 4 officers and 8 jawans. in how many ways can 6 be selected, so that:
(a) exactly one officer is included? (b) at least 2 officers are included?

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242.

Show that; $straight C presuperscript straight n subscript straight r space equals space straight n over straight r space straight C presuperscript straight n minus 1 end presuperscript subscript straight r minus 1 end subscript.$

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243.

If $straight C presuperscript 16 subscript straight r space equals space straight C presuperscript 16 subscript straight r minus 2 end subscript comma$ find $space straight C presuperscript straight r subscript 4.$

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244.

If $straight alpha space equals space straight C presuperscript straight m subscript 2 comma$ find the value of $straight C presuperscript straight alpha subscript 2.$

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245.

Evaluate:

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

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246.

If $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ and $straight C presuperscript straight n subscript straight r equals 120$ , find value of $straight C presuperscript 6 subscript straight r$

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247. There are 5 doors in a room, 2 on one side and 3 on the other side. A man wishes to enter the room from the side with two doors and get out from the other side. In how many ways can this be done?

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Multiple Choice Questions

248.

The number of integers greater than 6000 that can be formed, using the digits 3,5,6,7 and 8 without repetition, is

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249.

If m is the AMN of two distinct real numbers l and n (l,n>1) and G₁, G₂, and G3 are three geometric means between l and n, then $straight G subscript 1 superscript 4 space plus 2 straight G subscript 2 superscript 4 space plus space straight G subscript 3 superscript 4$ equals

4l² mn
4lm²n
4 lmn²
4 lmn²

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250.
How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent?

8 . ⁶C₄ . ⁷C₄

6 . 7 . ⁸C₄

6 . 8 . ⁷C₄

6 . 8 . ⁷C₄

6 . 8 . ⁷C₄

Other than S, seven letters M, I, I, I, P, P, I can be arranged in 7!/2! 4!=7 . 5 . 3.

Now four S can be placed in 8 spaces in 8 C4 ways. Desired number of ways = 7 . 5 . 3 . ⁸C4 = 7 . ⁶C4 . ⁸C4.

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