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Home » From Frozen to Frozen: The Most Shocking Unreleased ‘Let It Go’ Lyrics You Need to Know! - 500apps

From Frozen to Frozen: The Most Shocking Unreleased ‘Let It Go’ Lyrics You Need to Know! - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 This implies $x \equiv \pm5 \pmod{10}$. Testing $x = 5$: $5^2 = 25$ ends in 25.

📌 Thus, the smallest such integer is $\boxed{5}$.Question: An entomologist studies 5 species of bees, 3 species of wasps, and 2 species of beetles. If she observes one species per day for 10 days, how many distinct observation sequences are possible if species within each category are indistinguishable?

📌 Solution: The problem requires calculating the number of distinct permutations of 10 items where there are 5 identical bees, 3 identical wasps, and 2 identical beetles. The formula for multinomial coefficients applies:

📌 \frac{10!}{5! \cdot 3! \cdot 2!} = \frac{3628800}{120 \cdot 6 \cdot 2} = \frac{3628800}{1440} = 2520

📌 The number of distinct observation sequences is $\boxed{2520}$.

📌 Question: A science communicator creates a 10-part video series with 4 documentaries, 3 animations, and 3 interviews. If the order of video types matters but identical types are indistinct, how many unique sequences can be arranged?

📌 Solution: This is a multinomial permutation problem. The total sequences are given by:

📌 \frac{10!}{4! \cdot 3! \cdot 3!} = \frac{3628800}{24 \cdot 6 \cdot 6} = \frac{3628800}{864} = 4200

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