The number of ways to distribute 5 different toys among 3 children (each child may receive any number of toys) is 243. Which of the following quantities also equals 243?

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Number of subsets A of {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} such that no two elements of A sum to 11. Main count: 3⁵ = 243. Option A: The set {1,...,10} splits into 5 complementary pairs summing to 11: (1,10),(2,9),(3,8),(4,7),(5,6). For each pair, include neither, left only, or right only = 3 choices. Total = 3⁵ = 243. Option B: 2310 = 2*3*5*7*11 (five distinct primes). Number of ordered triples (x,y,z) with x*y*z = 2310 (positive integers): each prime factor goes to exactly one of x,y,z -> 3 choices per prime -> 3⁵ = 243. Option C: 6-digit number < 200000 using {1,2,3}: first digit must be 1; remaining 5 digits each from {1,2,3} -> 3⁵ = 243. Option D: for each of 5 questions choose original, al

The number of ways to distribute 5 different toys among 3 children (each child may receive any number of toys) is 243. Which of the following quantities also equals 243?

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