Fill the places, then count
"Fill the places, then count" is a free, interactive Class 11 Maths simulation for JEE, built on the lesson "Permutations of distinct objects" in Permutations and Combinations. Pick n objects and r places. The number under each place is how many objects are still free for it. Switch between ordered without repeats, ordered with repeats, and unordered selections. Ordered without repeats: n(n − 1)… for r places, nPr. With repeats: nʳ. Unordered: divide the ordered count by r!, which gives nCr. JEE Main asked 47 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Permutations of distinct objects 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 §6.3, §6.3.1, §6.3.3
- A permutation is an arrangement of objects in a definite order, using some or all of them. Changing the order gives a different permutation.
- nPr counts ordered arrangements of r things drawn from n different things with no repeats: nPr = n(n − 1)(n − 2) … (n − r + 1) = n!/(n − r)!, for 0 ≤ r ≤ n.
- Special cases: nPn = n!/0! = n!, and nP0 = 1, since there is exactly one way to arrange nothing.
- If repetition is allowed, each of the r places has all n choices, so the number of arrangements is nʳ.
- Sports day: a captain and a vice-captain are chosen from 12 students, one post each. The order matters (the two posts differ), so the count is 12P2 = 12 × 11 = 132.
- Relay: 4 of 7 sprinters are placed in running order as first, second, third and fourth legs: 7P4 = 7 × 6 × 5 × 4 = 840 line-ups.
- Words from the letters of MEDAL (5 different letters): 3-letter words 5P3 = 60, 5-letter words 5! = 120, and 3-letter words with repetition allowed 5³ = 125.
- Solving for n: if nP2 = 56, then n(n − 1) = 56 = 8 × 7, so n = 8.
Questions
3 answers
- What does the "Fill the places, then count" simulation show?
- Pick n objects and r places. The number under each place is how many objects are still free for it. Switch between ordered without repeats, ordered with repeats, and unordered selections.
- 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 "Permutations of distinct objects" in Permutations and Combinations (Class 11 Maths).
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