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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 ^{26}P_{2}

= `(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^{9}P_{2} = `(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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