Selections, and the orders inside them
"Selections, and the orders inside them" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Combinations" in Permutations and Combinations. Pick r of n labelled chips; each selection is shown with its r! orderings stacked beneath it, so nPr = nCr × r! is seen as grouping. JEE Main asked 47 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Combinations in Permutations and Combinations. Change the values and watch what happens.
What it shows
NCERT §6.4
Pick r of n labelled chips; each selection is shown with its r! orderings stacked beneath it, so nPr = nCr × r! is seen as grouping.
Controls
3 to try
- Steppern 2–7
- Stepperr 1–4
- Toggleshow orderings under each selection
Try this
Set up the relay: make the display show 35 teams and 840 running orders (n = 7, r = 4).
Common mistake
Using nCr for distinct posts or nPr for a team.
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
- A combination is a selection in which order does not matter: choosing A and B is the same as choosing B and A.
- nCr = n!/(r!(n − r)!), for 0 ≤ r ≤ n. It links to permutations by nPr = nCr × r!, because each selection of r objects can be put in order in r! ways.
- Relay: the team of 4 from 7 sprinters can be picked in 7C4 = 35 ways. Each team has 4! = 24 running orders, and 35 × 24 = 840 = 7P4.
- Handshakes: 10 house captains each shake hands once with every other: 10C2 = 45 handshakes.
- Points on a circle: 8 points give 8C2 = 28 chords and 8C3 = 56 triangles, since no three of them lie on a line.
- nC0 = 1 and nCn = 1: there is one way to choose nothing and one way to choose everything. A committee of 3 from 6 volunteers can be picked in 6C3 = 20 ways.
Questions
4 answers
- What does the "Selections, and the orders inside them" simulation show?
- Pick r of n labelled chips; each selection is shown with its r! orderings stacked beneath it, so nPr = nCr × r! is seen as grouping.
- What mistake does the "Selections, and the orders inside them" simulation fix?
- A common mistake it clears up: using nCr for distinct posts or nPr for a team.
- 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 "Combinations" in Permutations and Combinations (Class 11 Maths).
Embed this simulation
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