Answer:
i) There are 40320 possible orders
ii) There are 336 possible orders for the first 3 positions.
Step-by-step explanation:
Given: The number of finalists = 8
The number of boys = 3
The number of girls = 5
To find the number of sample point the sample space S for the number of possible orders, we need to find factorial of 8!
The number of possible orders = 8!
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8
= 40320
ii) From all 8 finalist, we need to choose first 3 position. Here the order is important. So we use permutation.
nPr =[tex]\frac{n!}{(n - r)!}[/tex]
Here n = 8 and r = 3
Plug in n =8 and r = 3 in the above formula, we get
8P3 = [tex]\frac{8!}{(8 - 3)!}[/tex]
= [tex]\frac{8!}{5!} \\= \frac{1.2.3.4.5.6.7.8}{1.2.3.4.5}[/tex]
= 6.7.8
= 336
So there are 336 possible orders for the first 3 positions.
