Answer :
To determine the number of possible final results for the best photograph contest, we can use the concept of permutations.
Given:
20 pictures were submitted to the contest.
The top 5 pictures will be placed in order from 1st to 5th.
To calculate the number of possible final results, we need to find the number of ways to select 5 pictures from the 20 pictures and arrange them in a specific order.
The formula for permutations is:
P(n, r) = n! / (n-r)!
where:
- n is the total number of items (pictures)
- r is the number of items selected (top 5 pictures)
In this case:
- n = 20 (total number of pictures)
- r = 5 (number of pictures selected for the top 5 positions)
Plugging in the values:
P(20, 5) = 20! / (20-5)!
= 20! / 15!
= 1,860,480
Therefore, there are 1,860,480 possible final results for the best photograph contest.
Answer:
1,860,480
Step-by-step explanation:
To find the number of possible final results for the top 5 photographs in the contest, we can use the concept of permutations without repetition.
Permutations deal with arrangements of objects where the order matters. This is applicable here, as each photograph can only be selected for one place in the ranking, and once a photograph is chosen for a certain place, it cannot be selected again for another place.
The permutation without repetition formula is:
[tex]P(n,r)=\dfrac{n!}{(n- r)!}[/tex]
where:
- n is total number of objects.
- r is the number of objects selected.
In this case, 20 pictures were submitted, so n = 20, and we are selecting the top 5, so r = 5.
Substitute the values into the formula:
[tex]P(20, 5)=\dfrac{20!}{(20-5)!}\\\\\\P(20, 5)=\dfrac{20!}{15!}\\\\\\P(20, 5)=\dfrac{20\times 19 \times 18 \times 17 \times16 \times15 \times 14 \times... \times3 \times2 \times1}{15 \times14 \times... \times3 \times2 \times1}\\\\\\P(20,5)=20\times 19 \times 18 \times 17 \times16\\\\\\P(20,5)=1860480[/tex]
Therefore, there are 1,860,480 possible final results for the top 5 photographs in the contest.
