You find 3 trees where each tree gives a

different coloured fruit: red, pink or orange. You perform crosses between all
three trees and get the following results:

P: red x pink ---F1: ½ red: ½ pink
P: red x orange --- F1: ½ red: ½ orange
P: pink x orange---F1: ¼ red: ¼ pink: ¼ orange:
¼ pale yellow

Are any of the plants true-breeding? How many different alleles for
fruit colour exist within these three trees?

To determine if any of the plants are true-breeding and the number of different alleles for fruit color, we need to analyze the results of the crosses.

From the given information, we can summarize the outcomes of the crosses as follows:

1. Red x Pink cross (P: red x pink) results in F1 offspring with ½ red and ½ pink fruits.
2. Red x Orange cross (P: red x orange) results in F1 offspring with ½ red and ½ orange fruits.
3. Pink x Orange cross (P: pink x orange) results in F1 offspring with ¼ red, ¼ pink, ¼ orange, and ¼ pale yellow fruits.

Now, let's look at each cross individually to determine if any plants are true-breeding:

1. Red x Pink cross (P: red x pink) - Since the F1 offspring yield both red and pink fruits, none of the plants are true-breeding for fruit color.

2. Red x Orange cross (P: red x orange) - Similar to the first cross, the F1 offspring produce both red and orange fruits. Hence, none of the plants are true-breeding for fruit color in this cross as well.

3. Pink x Orange cross (P: pink x orange) - In this cross, the F1 offspring exhibit four different fruit colors: red, pink, orange, and pale yellow. Therefore, no true-breeding plants for fruit color exist in this cross either.

Next, let's determine the number of different alleles for fruit color within these three trees. Alleles are alternate forms of a gene that determine a trait (in this case, fruit color).

Since we have observed three different fruit colors (red, pink, and orange) in the offspring, it can be inferred that there are at least three alleles (variants of a gene) for fruit color present within these three trees.

In summary:
- None of the plants resulting from the crosses are true-breeding for fruit color.
- The number of different alleles for fruit color within these three trees is at least three (red, pink, and orange).