A herpetologist is studying 7 distinct species of reptiles and 5 distinct species of amphibians. If she wants to photo one reptile and one amphibian each day for a week, in how many different ways can she schedule the photo sessions for 7 days with no repetition of the same pair?

Sat, 18 Apr 2026 20:18:56 +0000

A herpetologist is studying 7 distinct reptile species and 5 distinct amphibian species—an ongoing effort that fuels growing interest across science, nature, and digital communities. With biodiversity facing increasing attention in conservation and education circles, tracking rare species through field photography has become both a professional pursuit and a storytelling opportunity. Photographing one reptile and one amphibian each day offers a practical way to document daily discoveries, engage an audience, and contribute to public awareness. This routine naturally raises a precise logistical question: how many unique ways can she schedule 7 distinct daily photo sessions—one reptile and one amphibian—without repeating any species pairing over the week? The beauty of this setup lies not just in the numbers, but in the complexity: 7 reptiles pair with 5 amphibians, creating 35 total potential pairs. Choosing 7 unique daily pairings from these pairs without duplication tests both bandwidth and creativity—an instructive metric in planning fieldwork and digital content calendars. ### How It Actually Works Every day, the herpetologist selects a reptile and an amphibian species to photograph. Since no pair can repeat, each reptile-amphibian duo can appear at most once. The core challenge is permutation with restrictions—choosing 7 pairings from a set of 35 possible combinations, such that no species is repeated in the same day’s mix.