Where a word sits in the dictionary
"Where a word sits in the dictionary" is a free, interactive Class 11 Maths simulation for JEE, built on the NCERT section "Selecting then arranging, and dictionary order" in Permutations and Combinations. Dictionary listing grouped into blocks by first letter, then second; blocks before the target word collapse to counts like 3 × 4!. JEE Main asked 47 questions from this chapter across the 42 shifts Lumi has analysed (2017–2026).
From the lesson Selecting then arranging, and dictionary order in Permutations and Combinations. Change the values and watch what happens.
What it shows
NCERT §6.4
Dictionary listing grouped into blocks by first letter, then second; blocks before the target word collapse to counts like 3 × 4!.
Controls
2 to try
- Text-chipspick a word from a set of 5-letter words with distinct letters
- Buttonnext block
Try this
Find the rank of RELAY by stepping through the blocks to reach 81.
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
- Many problems need both steps: first choose (combinations), then arrange the chosen objects (permutations).
- Words with 2 vowels and 2 consonants from 4 vowels and 5 consonants: choose in 4C2 × 5C2 = 6 × 10 = 60 ways, then arrange the 4 letters in 4! = 24 ways, giving 60 × 24 = 1440 words.
- Dictionary order lists words by their first letter, then second, and so on. The letters of RELAY in alphabetical order are A, E, L, R, Y; the first word is AELRY and the last is YRLEA.
- Rank of RELAY: words starting with A, E or L: 3 × 4! = 72. Then words starting R A: 3! = 6. Then words starting R E A: 2! = 2, namely REALY and REAYL. RELAY comes next, so its rank is 72 + 6 + 2 + 1 = 81.
- The same block-by-block counting answers 'how many numbers are greater than …' questions: count by the first digit, then the next, fixing one place at a time.
Questions
3 answers
- What does the "Where a word sits in the dictionary" simulation show?
- Dictionary listing grouped into blocks by first letter, then second; blocks before the target word collapse to counts like 3 × 4!.
- 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 "Selecting then arranging, and dictionary order" in Permutations and Combinations (Class 11 Maths).
Embed this simulation
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