How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Solution:

No. of letters in the word "EQUATION" = 8 = n.
No.of letters in each word should be, r = 8.

Since arrangement matters in forming a word, we use the permutation. i.e., we use the nPr formula to find the required number of words.
Required no. of words = ⁸P₈
= 8!/(8 - 8)!
= 8!/(0)!
= 8×7×6×5×4×3×2×1
= 40,320

NCERT Solutions Class 11 Maths Chapter 7 Exercise 7.3 Question 8

How many words, with or without meaning, can be formed using all the letters of the word EQUATION, using each letter exactly once?

Summary:

The number of words, with or without meaning, that can be formed using all the letters of the word EQUATION, using each letter exactly once is 40,320.