Adam wrote down a 9-digit university roll number on a piece of paper. On his way home from office, it rained heavily and the paper got wet. Later, he saw that the first 4 digits of the roll number had disappeared. In how many ways can Adam complete this university roll number if repetition of digits is allowed?9⁴4!10⁴10³ x 9
Question
Adam wrote down a 9-digit university roll number on a piece of paper. On his way home from office, it rained heavily and the paper got wet. Later, he saw that the first 4 digits of the roll number had disappeared. In how many ways can Adam complete this university roll number if repetition of digits is allowed?9⁴4!10⁴10³ x 9
Solution
Adam can complete the university roll number in 10,000 ways. Here's why:
Since the first 4 digits of the roll number have disappeared and repetition of digits is allowed, Adam can choose any digit from 0 to 9 for each of the 4 missing digits.
Since there are 10 possibilities for each digit (0-9), and 4 digits are missing, the total number of ways to complete the roll number is 10^4, which equals 10,000.
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