How many 4-digit numbers are possible if the hundreds digit is 8 and if repetition of digits is allowed?
A) 100
B) 1,000
C) 9,000
D) 900
E) 1,800
1000
To find the number of 4-digit numbers with the hundreds digit as 8 and with repetition of digits allowed, we need to consider all the possible values for the thousands, tens, and ones digits.
For the thousands digit, we have 10 possible values (0 to 9), since repetition is allowed.
For the tens and ones digits, we also have 10 possible values each.
Therefore, the total number of possible 4-digit numbers is: 10 * 10 * 10 = 1,000.
Hence, the correct answer is B) 1,000.
To determine how many 4-digit numbers are possible with a given condition, we need to consider the possible values for each digit.
In this case, the hundreds digit is fixed at 8. So we only need to consider the values for the other three digits: thousands, tens, and units.
For each of these three digits, repetition of digits is allowed, which means we can choose any digit from 0 to 9 for each position.
For the thousands digit, we have 10 options (0 to 9), as any digit is allowed.
For the tens digit, we also have 10 options (0 to 9), as any digit is allowed.
For the units digit, we again have 10 options (0 to 9), as any digit is allowed.
Therefore, the total number of possible 4-digit numbers is obtained by multiplying the number of options for each digit:
10 (thousands) * 10 (tens) * 10 (units) = 1,000.
Therefore, the answer is B) 1,000.