How many 4-digit numbers are there having all digits as odd?

Question

Question

This question was previously asked in

NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)

Answer 1

Concept:

Counting 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. $5 \times 5 \times 5 \times 5$ $5 \times 5 \times 5 \times 5$

$5 \times 5 \times 5 \times 5$ $5 \times 5 = 25$ $125 \times 5 = 625$