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Permutations and Combinations

Short Answer Type

71. How many 3-digit numbers can be formed by using digits 1 to 9 if no digit is repeated?

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72.

How many 4-digit numbers are there if no digit is repeated?

How many numbers are there between 1000 and 9999 so that no digit is repeated?

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73. How many words with or without meaning can be formed using all the letters of the word ‘EQUATION’ using each letter exactly once?

Additional part: How many of these words begin with E and end with N?

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74. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if 4 letters are used at a time.

103 Views

75. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used at a time.

rightwards double arrow

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76. How many words with or without meaning can be formed using all the letters of the word ‘MONDAY’ assuming, that no letter is repeated, if all letters are used but the first letter is a vowel?

Number of letters in word 'Monday' = 6 (all distinct)

Number of vowels = 2 (O and A)

All six letters to be used but first letter is a vowel.

$rightwards double arrow$

Number of arrangements for a vowel in box 1 = $straight P presuperscript 2 subscript 1 space equals space fraction numerator 2 factorial over denominator 1 factorial end fraction equals 2$ ...(i)
(Two vowels and one box)

We are left with 5 letters and 5 boxes.

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

= 2 x 120 = 240

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77. How many words, with or without meaning, can be formed with the letters of word ‘MONDAY’ assuming, that no letter is repeated, if 4 letters are used but the first letter is a vowel ?

145 Views

78.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that the vowels and consonants occur together?

126 Views

79.

How many words, with or without meaning, can be formed using all the letters of the word EQUATION at a time so that no two consonants are together.

132 Views

80. In how many ways can 6-girls and 4 boys be seated in a row so that no two boys are together?

128 Views