Patterns in the table of nCr
"Patterns in the table of nCr" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Properties of combinations" in Permutations and Combinations. Row n lists nC0, nC1, …, nCn. Pick n and r: the orange cell is nCr, the green cell is its mirror nC(n − r), and the two blue cells just above add up to it. NCr = nC(n − r), and nCr = (n − 1)C(r − 1) + (n − 1)Cr. Each row is symmetric and peaks in the middle. JEE Main asked 47 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Properties of combinations in Permutations and Combinations. Change the values and watch what happens.
In JEE Main
42 shifts analysed
47 questions from Permutations and Combinations across the 42 JEE Main shifts Lumi has analysed (2017–2026).
The idea behind it
NCERT §6.4
- nCr = nC(n − r): choosing r objects to take is the same as choosing n − r objects to leave. So 10C8 = 10C2 = 45.
- If nCa = nCb, then a = b or a + b = n. If nC7 = nC5, then n = 12, and 12C2 = 66.
- Pascal's rule: nCr + nC(r − 1) = (n + 1)Cr. For example 5C2 + 5C1 = 10 + 5 = 15 = 6C2.
- The values nC0, nC1, …, nCn rise to the middle and fall back symmetrically. For n = 8 they are 1, 8, 28, 56, 70, 56, 28, 8, 1, with the largest, 70, at r = 4.
- Taking at least one of 6 different things: 6C1 + 6C2 + … + 6C6 = 6 + 15 + 20 + 15 + 6 + 1 = 63.
Questions
3 answers
- What does the "Patterns in the table of nCr" simulation show?
- Row n lists nC0, nC1, …, nCn. Pick n and r: the orange cell is nCr, the green cell is its mirror nC(n − r), and the two blue cells just above add up to it.
- Does JEE Main ask questions from Permutations and Combinations?
- Yes. JEE Main asked 47 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
- Is this simulation free?
- Yes. It is free and runs in the browser on a phone or a laptop. It belongs to the lesson "Properties of combinations" in Permutations and Combinations (Class 11 Maths).
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