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Ten different letters of an alphabet are given. Five-letter words are formed from these given letters. The number of words which have at least one letter repeated is
Correct answer is '69760'. Can you explain this answer?
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Ten different letters of an alphabet are given. Five-letter words are...
Given information:
- Ten different letters of an alphabet are given.
- Five-letter words are formed from these given letters.
To find:
The number of words which have at least one letter repeated.
Solution:
To find the number of words that have at least one letter repeated, we can use the concept of complementary counting.
Step 1: Find the total number of possible 5-letter words:
Since we have ten different letters, we can choose any one of them for each position in the word. Therefore, the total number of possible 5-letter words is 10^5 = 100,000.
Step 2: Find the number of words with no repeated letters:
For the first letter, we can choose any one of the ten letters.
For the second letter, we can choose any one of the remaining nine letters.
Similarly, for the third, fourth, and fifth letters, we can choose from the remaining eight, seven, and six letters respectively.
Therefore, the number of words with no repeated letters is 10 * 9 * 8 * 7 * 6 = 30,240.
Step 3: Find the number of words with at least one letter repeated:
To find the number of words with at least one letter repeated, we subtract the number of words with no repeated letters from the total number of possible words.
Number of words with at least one letter repeated = Total number of possible words - Number of words with no repeated letters
= 100,000 - 30,240
= 69,760.
Therefore, the number of words that have at least one letter repeated is 69,760.
- Ten different letters of an alphabet are given.
- Five-letter words are formed from these given letters.
To find:
The number of words which have at least one letter repeated.
Solution:
To find the number of words that have at least one letter repeated, we can use the concept of complementary counting.
Step 1: Find the total number of possible 5-letter words:
Since we have ten different letters, we can choose any one of them for each position in the word. Therefore, the total number of possible 5-letter words is 10^5 = 100,000.
Step 2: Find the number of words with no repeated letters:
For the first letter, we can choose any one of the ten letters.
For the second letter, we can choose any one of the remaining nine letters.
Similarly, for the third, fourth, and fifth letters, we can choose from the remaining eight, seven, and six letters respectively.
Therefore, the number of words with no repeated letters is 10 * 9 * 8 * 7 * 6 = 30,240.
Step 3: Find the number of words with at least one letter repeated:
To find the number of words with at least one letter repeated, we subtract the number of words with no repeated letters from the total number of possible words.
Number of words with at least one letter repeated = Total number of possible words - Number of words with no repeated letters
= 100,000 - 30,240
= 69,760.
Therefore, the number of words that have at least one letter repeated is 69,760.
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Community Answer
Ten different letters of an alphabet are given. Five-letter words are...
Number of 5-letter words with at least one letter repeated
= Total number of 5-letter words - Number of 5-letter words with all different letters
= 105 - 10P5
= 69,760
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Ten different letters of an alphabet are given. Five-letter words are formed from these given letters. The number of words which have at least one letter repeated isCorrect answer is '69760'. Can you explain this answer?
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Ten different letters of an alphabet are given. Five-letter words are formed from these given letters. The number of words which have at least one letter repeated isCorrect answer is '69760'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Ten different letters of an alphabet are given. Five-letter words are formed from these given letters. The number of words which have at least one letter repeated isCorrect answer is '69760'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Ten different letters of an alphabet are given. Five-letter words are formed from these given letters. The number of words which have at least one letter repeated isCorrect answer is '69760'. Can you explain this answer?.
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