Step-by-step explanation:
since there are 26 letters in the alphabet
and there are 10 numbers
without restrictions
10×10×10×26×26×26×10×10×10=17,576,000,000 reservation numbers are possible
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. The number of different reservation numbers that are possible is 17,576 × 10⁶.
Multiplication is the process of multiplying, therefore, adding a number to itself for the number of times stated. For example, 3 × 4 means 3 is added to itself 4 times, and vice versa for the other number.
Given that A hotel reservation number consists of 3 digits, followed by 3 letters, followed by 3 digits.
Since each place can be taken by the digits each place will have 10 possible outcomes, [0,9]. Similarly for each place that can be taken by the alphabet can be taken by 26 different digits.
Therefore, the number of different reservation numbers that are possible is,
Number of different reservations = 10 × 10 × 10 × 26 × 26 × 26 × 10 × 10 × 10
= 17,576 × 10⁶
Hence, the number of different reservation numbers that are possible is 17,576 × 10⁶.
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