Thu, 16 Apr 2026 07:58:43 +0000

A botanical garden has 7 distinct types of flowers. In how many ways can a gardener select 3 different types to create a visually appealing bouquet?
This engaging question reflects a growing curiosity among plant lovers and design enthusiasts who explore floral arrangements as both art and science. With the rise of aesthetic lifestyle trends and community-driven green spaces, selecting combinations of flowers thoughtfully has become a popular way to personalize outdoor or indoor gardens. So, how many unique selections are possible, and what does this choice really mean? On a botanical scale, this query taps into a broader cultural shift toward creative self-expression through nature. In the US, floral design—especially around seasonal blooms and curated bouquets—has gained traction across social platforms and lifestyle blogs. Selecting three distinct flowers invites a focus on contrast, color harmony, and seasonal availability,ではなく just single-species purchases. This accessible but meaningful decision supports both hobbyists and professionals in crafting memorable garden displays. Now, let’s unpack the math behind the floral choice.
When selecting 3 distinct flowers from 7, the order doesn’t matter—only which flowers are chosen, making this a classic combination problem. The number of ways is calculated using the combination formula: C(n, k) = n! / (k!(n – k)!), where **n = 7** and **k = 3**.
So, C(7, 3) = 7! / (3! × 4!) = (7 × 6 × 5) / (3 × 2 × 1) = 210 / 6 = 35.
There are 35 unique combinations of three flower types to create a visually appealing bouquet from seven distinct options. How A botanical garden has 7 distinct types of flowers. In how many ways can a gardener select 3 different types to create a visually appealing bouquet?
Actually works through precise combinatorial logic.
- Sort available species by bloom season, height, or color family
- Apply C(7,3) to determine all non-repeating, unordered groupings
- Recognize each set offers a distinct aesthetic arrangement
This method guarantees a customized, balanced bouquet without repetition or confusion.