Question 19 of 42beginner🔧 ApplyNumerical2 marks

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

Correct Answer

40320

Exercise: EXERCISE 6.3 | Q: 8 | (Page 15)
For More Understanding

Explanation

This is a permutation problem where we need to arrange all letters of the word EQUATION. The word EQUATION has 8 distinct letters: E, Q, U, A, T, I, O, N. Since all letters are different and each letter must be used exactly once, we need to find the number of arrangements of 8 distinct objects taken all at a time. This is calculated as 8! (8 factorial).

Solution Steps

  1. Step 1: Count the total number of letters in the word EQUATION. The word has 8 letters: E, Q, U, A, T, I, O, N.

  2. Step 2: Check if any letter is repeated. All 8 letters are distinct (no repetition).

  3. Step 3: Apply the formula for arranging n distinct objects taken all at a time, which is n!.

  4. Step 4: Calculate 8! = 8×78 \times 7 × 6×56 \times 5 × 4×34 \times 3 × 2×12 \times 1 = 40320.

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