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Home » 100 The Hundred: The Hidden Secrets Counting to Endless Wonders! - Treasure Valley Movers

100 The Hundred: The Hidden Secrets Counting to Endless Wonders! - Treasure Valley Movers

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 Solution: We are given 3 toucans (T), 2 tanagers (A), 1 macaw (M), and 1 hummingbird (H), and we want to count the number of distinct sequences of length 7 using these indistinguishable items. The total number of distinct permutations of a multiset is given by:

📌 Question: A science educator has 4 identical solar-powered robots, 3 identical motion detectors, and 2 identical light sensors to distribute across 9 classroom stations for a hands-on robotics activity. If each station receives exactly one device, how many distinct ways can the devices be assigned?

📌 Solution: We are assigning 4 identical robots (R), 3 identical detectors (D), and 2 identical sensors (S) to 9 distinct stations, with one device per station. This is a multinomial coefficient problem:

📌 Question: An ice cream truck offers 8 different eco-friendly flavors and 5 organic toppings. If a customer chooses 2 different flavors and 2 different toppings, how many unique combinations can they order?

📌 Solution: To choose 2 different flavors from 8, the number of combinations is:

📌 To choose 2 different toppings from 5:

📌 Since flavor and topping choices are independent, the total number of unique combinations is:

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