Determine , apermutation or combination
1.The winner and second and third placed in contest woth 10 finalists .
2.Selecting nine books to check out of the library from a reading list of twelve .
3.Selecting three of fifteen flavours of ice cream .
4.An arrangement of letters in the word ( aloha ).
what do you think? Your previous question was just like this, and good solutions were given.
show us the reasoning behind your choices, and we can fix any mis-steps.
1.P(10,1)*p(10,2)*p(10.3)
2.C(12,9)
3.C(15,3)
4.5!
the question was: choose permutation or combination
Based on your answers, I'd say you chose P,C,C,P, which is correct.
However for #1, you have 10 finalists, and you want the number of ways to pick 3 of them. That is just P(10,3), which is in fact 10*9*8 (10!/7!).
There are 10 ways to wick a winner, leaving just 9 choices for runner-up, and 8 choices for 3rd place.
Other than that, your answers look good.
To determine whether each scenario represents a permutation or combination, we need to understand the difference between the two.
Permutation: A permutation is an arrangement of objects in a specific order. The order in which the objects are arranged matters.
Combination: A combination is a selection of objects where the order does not matter. The focus is on choosing a group of objects, regardless of the order.
Now let's analyze each scenario:
1. The winner and second and third placed in a contest with 10 finalists.
This scenario represents a permutation because the order of the winners matters. The first, second, and third places have different rankings, and their order is relevant.
2. Selecting nine books to check out of the library from a reading list of twelve.
This scenario represents a combination because the order of the books does not matter. The focus is on selecting a group of books, regardless of the order in which they are chosen.
3. Selecting three of fifteen flavors of ice cream.
This scenario also represents a combination because the order of the ice cream flavors does not matter. Only the selection of three flavors is important.
4. An arrangement of letters in the word "ALOHA".
This scenario represents a permutation because the arrangement of the letters matters. The order of the letters in the word "ALOHA" can be changed to create different permutations.
To determine whether a scenario represents a permutation or combination, consider whether the order of the items matters or not.