Question:
In how many ways can the letters of the word 'PEANUT' be arranged?
In how many ways can the letters of the word 'PEANUT' be arranged?
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Memorizing factorials up to 7! is very helpful for competitive exams: $1!=1, 2!=2, 3!=6, 4!=24, 5!=120, 6!=720, 7!=5040$.
Updated On: Apr 20, 2026
- 360
- 720
- 700
- 840
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
The number of ways to arrange $n$ distinct objects is given by $n!$ (n factorial). This is a basic permutation problem where all items are unique.
Step 2: Key Formula or Approach:
Number of arrangements = $n!$, where $n$ is the number of letters.
Step 3: Detailed Explanation:
1. Count the number of letters in the word 'PEANUT'. 2. The letters are P, E, A, N, U, T. There are 6 letters. 3. Check for repetitions: All letters are distinct (unique). 4. Total arrangements = $6!$. \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 6! = 720. \]
Step 4: Final Answer:
The letters can be arranged in 720 ways.
The number of ways to arrange $n$ distinct objects is given by $n!$ (n factorial). This is a basic permutation problem where all items are unique.
Step 2: Key Formula or Approach:
Number of arrangements = $n!$, where $n$ is the number of letters.
Step 3: Detailed Explanation:
1. Count the number of letters in the word 'PEANUT'. 2. The letters are P, E, A, N, U, T. There are 6 letters. 3. Check for repetitions: All letters are distinct (unique). 4. Total arrangements = $6!$. \[ 6! = 6 \times 5 \times 4 \times 3 \times 2 \times 1 \] \[ 6! = 720. \]
Step 4: Final Answer:
The letters can be arranged in 720 ways.
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