A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words. - Mathematics and Statistics

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Sum

A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words.

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Solution

There are total of 26 alphabets.
A code word contains 2 English alphabets.
∴ 2 alphabets can be filled in 26P2
= `(26!)/((26-2)!)=(26xx25xx24!)/(24!)` = 650 way
Also, alphabets to be followed by two distinct non-zero digits from 1 to 9 which can be filled in
9P2 = `(9!)/((9-2)!)=(9xx8xx7!)/(7!)` = 72 ways
∴ Total number of a code words = 650 × 72 = 46800

Concept: Permutations - Permutations When Repetitions Are Allowed
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Chapter 6: Permutations and Combinations - Exercise 6.3 [Page 81]

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Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.3 | Q 13. (i) | Page 81
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