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the 10th amendment - Moon Smoking

📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 Question: A geologist is analyzing 5 different rock layers. If the layers are sampled in pairs and each pair is taken without replacement, how many different pairings are possible?

📌 Question: An ice cream truck offers 8 unique flavors and 5 types of toppings. How many different combinations of 3 flavors and 2 toppings can a customer choose?

📌 Question: Three distinct prime numbers less than 30 are selected at random. What is the probability that their sum is even?

📌 Solution: First, list all prime numbers less than 30:

📌 There are 10 primes. Only one is even: 2. The rest are odd. The sum of three numbers is even if either all three are even (impossible, since only one even prime) or exactly two are odd and one is even. But since only one even prime exists, the sum is even only when 2 is included and the other two are odd primes.

📌 So, for the sum to be even, the selected primes must include 2 and two odd primes.

📌 Number of favorable outcomes: choose 2 odd primes from the 9 odd ones:

📌 Total number of ways to choose any 3 primes from 10:

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