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Ten different letters of an alphabet are given. Words with 6 letters are formed with these alphabets. How many such words can be formed when repetition is not allowed in any word?
- a)52040
- b)21624
- c)182340
- d)151200
- e)600000
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Ten different letters of an alphabet are given. Words with 6 letters a...
To solve this problem, we can use the concept of permutations.
Permutations represent the number of possible arrangements of a set of objects. In this case, we have ten different letters to form words with 6 letters without repetition.
Let's break down the problem step by step:
Step 1: Determine the number of choices for the first letter.
Since repetition is not allowed, we have ten options for the first letter.
Step 2: Determine the number of choices for the second letter.
After selecting the first letter, we have nine remaining letters to choose from for the second letter.
Step 3: Determine the number of choices for the third letter.
Similarly, after selecting the first two letters, we have eight remaining letters to choose from for the third letter.
Step 4: Determine the number of choices for the fourth letter.
Following the same logic, we have seven remaining letters to choose from for the fourth letter.
Step 5: Determine the number of choices for the fifth letter.
After selecting the first four letters, we have six remaining letters to choose from for the fifth letter.
Step 6: Determine the number of choices for the sixth letter.
Finally, after selecting the first five letters, we have five remaining letters to choose from for the sixth letter.
Now, to find the total number of possible words, we need to multiply the number of choices at each step.
Total number of words = (10 choices for the first letter) * (9 choices for the second letter) * (8 choices for the third letter) * (7 choices for the fourth letter) * (6 choices for the fifth letter) * (5 choices for the sixth letter)
Total number of words = 10 * 9 * 8 * 7 * 6 * 5 = 151,200
Therefore, the correct answer is option D) 151,200.
Permutations represent the number of possible arrangements of a set of objects. In this case, we have ten different letters to form words with 6 letters without repetition.
Let's break down the problem step by step:
Step 1: Determine the number of choices for the first letter.
Since repetition is not allowed, we have ten options for the first letter.
Step 2: Determine the number of choices for the second letter.
After selecting the first letter, we have nine remaining letters to choose from for the second letter.
Step 3: Determine the number of choices for the third letter.
Similarly, after selecting the first two letters, we have eight remaining letters to choose from for the third letter.
Step 4: Determine the number of choices for the fourth letter.
Following the same logic, we have seven remaining letters to choose from for the fourth letter.
Step 5: Determine the number of choices for the fifth letter.
After selecting the first four letters, we have six remaining letters to choose from for the fifth letter.
Step 6: Determine the number of choices for the sixth letter.
Finally, after selecting the first five letters, we have five remaining letters to choose from for the sixth letter.
Now, to find the total number of possible words, we need to multiply the number of choices at each step.
Total number of words = (10 choices for the first letter) * (9 choices for the second letter) * (8 choices for the third letter) * (7 choices for the fourth letter) * (6 choices for the fifth letter) * (5 choices for the sixth letter)
Total number of words = 10 * 9 * 8 * 7 * 6 * 5 = 151,200
Therefore, the correct answer is option D) 151,200.
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Ten different letters of an alphabet are given. Words with 6 letters are formed with these alphabets. How many such words can be formed when repetition is not allowed in any word?a)52040b)21624c)182340d)151200e)600000Correct answer is option 'D'. Can you explain this answer?
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