When it was 70 degrees outside, 50 members showed up at a beach club. For each degree the temperature rose, another 10 members c

Answer:

i) A total of 40320 different arrangements

ii) For the initial 3 spots, there are 336 different combinations.

Step-by-step explanation:

Given: The total finalists = 8

The count of boys = 3

The count of girls = 5

To determine the number of sample point in the sample space S for possible arrangements, we calculate the factorial of 8!

The number of possible arrangements equals 8!

= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8

= 40320

ii) Among the 8 finalists, we must select the first 3 spots. The sequence matters, hence we utilize permutation.

nPr =

Here n = 8 and r = 3

Substituting n = 8 and r = 3 into the formula, we arrive at

8P3 =

=

= 6.7.8

= 336

Thus, there are 336 different arrangements for the first 3 spots.