Question
Download Solution PDFHow many 4-digit numbers are there having all digits as odd?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCounting 4-digit Numbers with All Odd Digits:
- Each digit in a 4-digit number can be one of the odd digits: 1, 3, 5, 7, or 9.
- There are 5 choices for each digit since there are 5 odd digits available.
- For a 4-digit number, we need to select a digit for each of the 4 positions independently.
- The total number of 4-digit numbers with all odd digits is the product of choices for each digit.
Calculation:
Given,
Choices for each digit = 5 (as the digits are 1, 3, 5, 7, 9)
Number of digits, n = 4
The total number of 4-digit numbers with all odd digits is,
\(5^4\) = 5 × 5 ×5 × 5 = 625
∴ 625 4-digit numbers have all digits as odd.
∴ The total number of 4-digit numbers with all odd digits is 625.
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