Question

An experiment consists of choosing objects without regards to order. Determine the size of the sample space when you choose the following:(a) 8 objects from 19(b) 3 objects from 25(c) 2 objects from 23

Answer 1

Answer:

a

    $n= 75, 582$

b

  $n= 2300$

c

  $n = 253$

Step-by-step explanation:

     Generally the size of the sample sample space is  mathematically represented as

           $n = \left N } \atop {}} \right. C_r$

Where   N is the total number of objects available and  r is the  number of objects to be selected

    So  for  a,  where N = 19  and r = 8  

         $n = \left 19 } \atop {}} \right. C_8 = \frac{19 !}{(19 - 8 )! 8!}$

                           $= \frac{19 *18 *17 *16 *15 *14 *13 *12 *11! }{11 ! \ 8!}$

                           $n= 75, 582$

    For  b  Where  N  = 25 and  r  =  3

           $n = \left 25 } \atop {}} \right. C_3 = \frac{25 !}{(19 - 3 )! 3!}$

                             $= \frac{25 *24 *23 *22 ! }{22 ! \ 3!}$

                             $n= 2300$

   For  c  Where  N  = 23 and  r  =  2

            $n = \left 23 } \atop {}} \right. C_2 = \frac{23 !}{(23 - 2 )! 2!}$

                              $= \frac{23 *22 *21! }{21 ! \ 3!}$

                              $n = 253$