To determine how many 4-digit numbers exist where all the digits are odd, we need to identify the possible choices for each digit position in a 4-digit number.
An odd digit can be one of the following numbers: 1, 3, 5, 7, or 9. Therefore, for any digit position, there are 5 possible choices.
Let's analyze each of the digit positions in the 4-digit number:
- Thousands Place: Since we're looking at a 4-digit number, the thousands place cannot be zero. It must be odd, and we have 5 choices (1, 3, 5, 7, 9).
- Hundreds Place: The hundreds place can also have any of those 5 odd numbers.
- Tens Place: Similarly, the tens place has 5 possibilities.
- Units Place: The units place also has 5 choices.
Using the basic principle of counting, the total number of 4-digit numbers with all digits odd is the product of the number of choices for each digit place.
5 \times 5 \times 5 \times 5 = 5^4 = 625
Thus, there are 625 4-digit numbers where all digits are odd. Therefore, the correct answer is: 625.
Similar Questions
- Three perfect dice \(D_1, D_2\) and \(D_3\) are rolled. Let \(x, y\) and \(z\) represent the numbers on \(D_1, D_2\) and \(D_3\) respectively. What is the number of possible outcomes such that \(x < y < z\)?
- A man has \(7\) relatives (\(4\) women and \(3\) men). His wife also has \(7\) relatives (\(3\) women and \(4\) men). In how many ways can they invite \(3\) women and \(3\) men so that \(3\) of them are man's relatives and \(3\) of them are his wife's relatives?
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Important Questions from Permutation and Combination
The following figure is made with nine squares of length 1 cm each.
A student is standing at point P. The total number of shortest paths to reach point Q from point P, if the student walks along the boundaries of the squares only, is:
Consider the following statements (all the angles are measured in degrees) :
1. If two supplementary angles are $4x + 40$ and $10x$, then $x$ is;
2. The complementary angle of $\frac{4}{5} \times 45$ is :
3. If two complementary angles are in the ratio of $4 : 5$, then the smallest angle is :
Which of the following is correct?
Codes:
1 2 3- There are 40 persons in a palace. If every person shakes hands with every other person, what will be the total number of handshakes?
- How many words can be formed with or without meaning by using all letters of the word DELHI?
A rectangular wall is divided into four squares of equal size where there are two rows each having two squares. The top left square is coloured with green. If, including green, there are three colours available and each square is coloured using any one of these three colours such that no two adjacent squares get painted with the same colour; then how many colour combinations are possible ?
