Permutations and Combinations

Permutations and Combinations

Question

The ages of the students in a class form an A.P. whose common difference is 4 months. If the youngest student is 8 years old and the sum of the ages of all the students in the class is 168 years. Find the numbers of students in the class.

Answer

Let the number of students in the class be n.
Let a be the age of youngest student
∴                              a = 8 years
Since the age of the students form an A.P. with common difference 4 months or 1 third years.
∴                             straight d equals space 1 third years
Since the sum of the ages of all the students in the class is 168 years.
∴                      straight S subscript straight n space equals space 168                rightwards double arrow space<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)
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#6 {main}</pre>
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#6 {main}</pre>                 rightwards double arrow     16 straight n plus fraction numerator straight n squared minus straight n over denominator 3 end fraction space equals space 336
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#6 {main}</pre>                    rightwards double arrow   straight n squared plus 47 straight n minus 1008 space equals space 0

rightwards double arrow                  space space straight n space equals space fraction numerator negative 47 plus-or-minus square root of left parenthesis 47 right parenthesis squared plus 4 left parenthesis 1 right parenthesis left parenthesis 1008 right parenthesis end root over denominator 2 left parenthesis 1 right parenthesis end fraction space equals space fraction numerator negative 47 plus-or-minus square root of 2209 plus 4032 end root over denominator 2 end fraction
                            space space equals space fraction numerator negative 47 plus-or-minus square root of 6241 over denominator 2 end fraction space equals space fraction numerator negative 47 plus-or-minus 79 over denominator 2 end fraction space equals space 32 over 2 comma space minus 126 over 2 space equals space 16 comma space minus 63
rightwards double arrow                     n = 16
∵   Number of students cannot be negative. Hence, number of students in the class is 16.

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