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

The size of the sample space can be determined using combinations.

Step-by-step explanation:

The sample space of an experiment where objects are chosen without regards to order can be determined using combinations.

For (a) choosing 8 objects from 19, the size of the sample space can be found using the combination formula:

Sample space = C(n, r) = C(19, 8) = 19! / (8! * (19-8)!) = 75582

Similarly, for (b) choosing 3 objects from 25, the sample space can be found using:

Sample space = C(25, 3) = 25! / (3! * (25-3)!) = 2300

And for (c) choosing 2 objects from 23, the sample space is:

Sample space = C(23, 2) = 23! / (2! * (23-2)!) = 253

Answer 2

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 = (19 !)/((19 - 8 )! 8!)`

`= (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 = (25 !)/((19 - 3 )! 3!)`

`= (25 *24 *23 *22 ! )/(22 ! \ 3!)`

`n= 2300`

For c Where N = 23 and r = 2

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

`= (23 *22 *21! )/(21 ! \ 3!)`

`n = 253`