Simulation · Maths · Class 11
Where a word sits in the dictionary
From the lesson Selecting then arranging, and dictionary order in Permutations and Combinations. Change the values and watch what happens.
Where a word sits in the dictionaryMaths · Class 11
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.