How many different four digit numbers are there in the octal (Base 8) system, expressed in that system?a)3584b)2058c)6000d)7000Correct answer is option 'D'. Can you explain this answer?

Question

Answer

Solution:

In the octal system, we have 8 digits ranging from 0 to 7. To count the number of different four-digit numbers, we need to count the number of choices we have for each of the four digits.

Counting the first digit: Since we cannot have a leading zero, we have 7 choices for the first digit (from 1 to 7).

Counting the remaining digits: For each of the remaining three digits, we have 8 choices (from 0 to 7).

Therefore, the total number of different four-digit numbers is:

7 × 8 × 8 × 8 = 7 × 512 = 3584

However, the question asks for the answer to be expressed in the octal system. Therefore, we need to convert the answer to octal:

3584 = 5 × 8^3 + 5 × 8^2 = 7000 (in octal)

Hence, the correct answer is option D, 7000.

Answer

Here the no. of digits will be 7*8*8*8 as initial no. can not be o and rest will be 0 to 7 so 8 no. now the result would be 3584 and then convert it to octal system. the and would be 7000

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