katrina has 3 apples, 2 oranges, and 1 peach in a cowl. if she randomly selects one apple and one orange to practice sketching and then puts the fruit back in the bowl then repeats the steps, What are all the possible combinations for the sketches she can make? list all the outcomes.

i got that there were 5 outcomes: aa,ao,ap,oo,op

but my i wasn't in class when we went over this and my friend wrote on my paper that there are 8 outcomes. if so ehat would they be and how do you get 8???

aa, ao, ap, oo, op

there are five, unless order is important:
aa, ao, ap, oo, op, oa, pa, po
and then there are eight.

thanks so much that's what i thought to. and it would be the same combination whether the order is backwords or forwards.

i know, but say order matters. as in, the first one picked is in the foreground and the second one picked is placed in the background. it would result in different sketches.

idontknow

To find all the possible combinations for the sketches Katrina can make, we need to consider the selection of one apple and one orange, with replacements (putting the fruit back into the bowl after each selection). Let's break down the process step by step:

Step 1: Select one fruit (apple or orange)
- There are three possibilities: apple (A), orange (O), or peach (P)

Step 2: Put the fruit back into the bowl
- After each selection, the fruit is returned to the bowl, so the total number of fruits remains the same.

To find the number of outcomes, we need to multiply the number of possibilities at each step.

Step 1 (1 fruit selection):
- Choose one fruit from three possibilities: 3 options (A, O, or P)

Step 2 (1 fruit selection):
- Choose one fruit from three possibilities: 3 options (A, O, or P)

Now, we need to count all the possible combinations. Every combination consists of one fruit selected in Step 1 and another fruit selected in Step 2. We will use the following notation: (fruit selected in Step 1, fruit selected in Step 2).

Possible combinations:
1. (A, A)
2. (A, O)
3. (A, P)
4. (O, A)
5. (O, O)
6. (O, P)
7. (P, A)
8. (P, O)

As you can see, there are eight possible combinations:
(A, A), (A, O), (A, P), (O, A), (O, O), (O, P), (P, A), (P, O).

Therefore, your friend was correct that there are eight outcomes, not five.