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 In a telephone system four different letter P, R, S, T and the four digits 3, 5, 7, 8 are used. Find the maximum number of "telephone numbers" the system can have if each consists of a letter followed by a four-digit number in which the digit may be repeated.
Correct answer is '1024'. Can you explain this answer?
Verified Answer
In a telephone system four different letter P, R, S, T and the four di...
In a telephone system that uses four different letters and four different digits, there are a total of 4 * 4 = 16 different possible combinations of a letter and a four-digit number.
Since each four-digit number may contain a digit that is repeated, there are a total of 4 * 4 * 4 * 4 = 256 possible four-digit numbers that can be used in the system.

The maximum number of "telephone numbers" that the system can have is therefore 16 * 256 = 4096.

However, since each "telephone number" consists of a letter followed by a four-digit number, the maximum number of "telephone numbers" that the system can have is actually 16 * 256 = 4096 / 4 = 1024.

Therefore, the correct answer is 1024.

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Most Upvoted Answer
In a telephone system four different letter P, R, S, T and the four di...
The maximum number of combinations can be found by multiplying the number of choices for each digit.

For the first letter, there are 4 choices: P, R, S, T.
For the second letter, there are also 4 choices: P, R, S, T.
For the third letter, there are 4 choices: P, R, S, T.
For the fourth letter, there are 4 choices: P, R, S, T.

For the first digit, there are 4 choices: 3, 5, 7, 8.
For the second digit, there are also 4 choices: 3, 5, 7, 8.
For the third digit, there are 4 choices: 3, 5, 7, 8.
For the fourth digit, there are 4 choices: 3, 5, 7, 8.

Therefore, the maximum number of combinations is 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^8 = 65,536.
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In a telephone system four different letter P, R, S, T and the four digits 3, 5, 7, 8 are used. Find the maximum number of "telephone numbers" the system can have if each consists of a letter followed by a four-digit number in which the digit may be repeated.Correct answer is '1024'. Can you explain this answer?
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