The government of Country $X$ uses a particular method to create a unique Identification Number (I

Question

The government of Country $X$ uses a particular method to create a unique Identification Number (IN) for each of its citizens. The IN consists of $4$ digits from $0$ to $9$ followed by one of the ten letters $A - J$. The digits in the IN can be repeated. Find the number of different Identification Numbers that can be created.[1] Suppose the letter at the end of the IN is determined by the following steps: Step 1: Find the sum of all the digits in the IN. Step 2: Divide the sum by $10$ and note the remainder. Step 3: Use the table below to determine the letter that corresponds to the remainder. Remainder $0$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ Letter A B C D E F G H I J It is known that all citizens who are born in the year $1990$ must have the digit '$9$' appearing twice in their IN and the sum of all the digits in their IN is at least $20$. Eric, who is born in the year $1990$, has 'I' as the last letter of his IN. Find the number of INs that could possibly belong to Eric.[4]

Accepted Answer

$100000$; $42$

Permutation and Combination - Permutations of Identical Objects

Permutation and Combination - Permutations of Identical Objects

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