Permutations & Combinations
Triplets with Distinct Non-negative Integers Summing to 15
nta_pyq_2023_apr
Grade 11
Question:
Number of triplets $(x,y,z)$ with distinct non-negative integers and $x+y+z=15$ is
Step-by-Step Solution
Key Concept: Total solutions of $x+y+z=15$ with non-negative integers: $\binom{17}{2}=136$. Subtract cases where at least two are equal.
114 triplets.
Correct Answer: 3