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How Many 4-letter Code Can Be Formed Using the First 10 Letters of the English Alphabet, If No Letter Can Be Repeat - CBSE (Arts) Class 11 - Mathematics

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ConceptFundamental Principle of Counting

Question

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeat

Solution

There are as many codes as there are ways of filling 4 vacant places   in succession by the first 10 letters of the English alphabet, keeping in mind that the repetition of letters is not allowed.

The first place can be filled in 10 different ways by any of the first 10 letters of the English alphabet following which, the second place can be filled in by any of the remaining letters in 9 different ways. The third place can be filled in by any of the remaining 8 letters in 8 different ways and the fourth place can be filled in by any of the remaining 7 letters in 7 different ways.

Therefore, by multiplication principle, the required numbers of ways in which 4 vacant places can be filled is 10 × 9 × 8 × 7 = 5040

Hence, 5040 four-letter codes can be formed using the first 10 letters of the English alphabet, if no letter is repeated.

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APPEARS IN

NCERT Solution for Mathematics Textbook for Class 11 (2018 to Current)
Chapter 7: Permutations and Combinations
Q: 3 | Page no. 138

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Solution How Many 4-letter Code Can Be Formed Using the First 10 Letters of the English Alphabet, If No Letter Can Be Repeat Concept: Fundamental Principle of Counting.
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