<p>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.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the number of different Identification Numbers that can be created.<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">Suppose the letter at the end of the IN is determined by the following steps:</div><div class="list-item-paragraph">Step 1: Find the sum of all the digits in the IN.<br>Step 2: Divide the sum by \(10\) and note the remainder.<br>Step 3: Use the table below to determine the letter that corresponds to the remainder.</div><div class="table-container"><table style="table-layout: fixed; width: 480px;"><colgroup><col style="width: 80px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"><col style="width: 40px;"></colgroup><thead><tr style="height: 40px;"><th style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>Remainder</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(0\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(1\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(2\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(3\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(4\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(5\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(6\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(7\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(8\)</p></th><th style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>\(9\)</p></th></tr></thead><tbody><tr style="height: 40px;"><td style="height: 40px; min-height: 40px; text-align: left; --cell-justify: flex-start"><p>Letter</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>A</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>B</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>C</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>D</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>E</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>F</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>G</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>H</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>I</p></td><td style="height: 40px; min-height: 40px; text-align: center; --cell-justify: center"><p>J</p></td></tr></tbody></table></div><div class="list-item-paragraph">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.<span class="inline-marks">[4]</span></div></li></ol>

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.

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.

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.

Permutation and Combination - Permutations of Identical Objects

Question 6818df43