Using combination formula, 15 different homes can be built.
For given question,
Let the three different interior plans be I1, I2 and I3
Let E1, E2, E3, E4 and E5 be five different exterior plans.
For each interior plan a developer has 3 choices.
Using combination formula,
As,
[tex]^{3}C_1\\\\=\frac{3!}{1!(3-1)!} \\\\=3[/tex]
And for each exterior plan a developer has 5 choices.
Using combination formula,
[tex]^{5}C_1\\\\=\frac{5!}{1!(5-1)!} \\\\=5[/tex]
Thus, for each interior plan a developer has 5 choices of exterior plan that is together 5 × 3 = 15 possibilities.
Therefore, using combination formula, 15 different homes can be built.
Learn more about the combination here:
https://brainly.com/question/13387529
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