How many 3 digit numbers are there, with distinct digits, with each of the digits odd?
How many 3 digit numbers are there, with distinct digits, with each of the digits odd?
Aniket Singh , 4 Months ago
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7 grade maths> How many 3 digit numbers are there, with ...
1 AnswersAskiitians Tutor Team
Last Activity: 4 Months ago
To solve this problem, we need to determine how many 3-digit numbers can be formed with distinct digits where each digit is odd.
Step 1: Identify the odd digits
The odd digits are 1, 3, 5, 7, and 9. These are the only digits that can be used in the 3-digit number.
Step 2: Determine the number of ways to choose the digits
For the hundreds place (the first digit), we can choose any of the 5 odd digits (1, 3, 5, 7, or 9).
For the tens place (the second digit), we need to choose a distinct digit from the remaining 4 odd digits.
For the ones place (the third digit), we need to choose a distinct digit from the remaining 3 odd digits.
Step 3: Calculate the total number of combinations
There are 5 choices for the hundreds place.
After choosing the hundreds place, there are 4 choices left for the tens place.
After choosing the tens place, there are 3 choices left for the ones place.
Thus, the total number of distinct 3-digit numbers with all odd digits is:
5 × 4 × 3 = 60
Final Answer:
There are 60 distinct 3-digit numbers where each digit is odd.
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Other Related Questions on 7 grade maths
To find how many two-digit numbers are divisible by both 2 and 3, we first determine the range of two-digit numbers, which is from 10 to 99.
A number that is divisible by both 2 and 3 is also divisible by 6 (since 6 is the least common multiple of 2 and 3).
The smallest two-digit number divisible by 6 is 12, and the largest is 96.
To find all the two-digit numbers divisible by 6, we can use the formula for the nth term of an arithmetic sequence:
- First term (a) = 12
- Common difference (d) = 6
- Last term (l) = 96
We can find the number of terms (n) in this sequence using the formula:
n = (l - a) / d + 1
Substituting the values:
n = (96 - 12) / 6 + 1 = 84 / 6 + 1 = 14 + 1 = 15
Thus, there are 15 two-digit numbers that are divisible by both 2 and 3.
To find how many two-digit numbers are divisible by both 2 and 3, we first determine the range of two-digit numbers, which is from 10 to 99.
A number that is divisible by both 2 and 3 is also divisible by 6 (since 6 is the least common multiple of 2 and 3).
The smallest two-digit number divisible by 6 is 12, and the largest is 96.
To find all the two-digit numbers divisible by 6, we can use the formula for the nth term of an arithmetic sequence:
- First term (a) = 12
- Common difference (d) = 6
- Last term (l) = 96
We can find the number of terms (n) in this sequence using the formula:
n = (l - a) / d + 1
Substituting the values:
n = (96 - 12) / 6 + 1 = 84 / 6 + 1 = 14 + 1 = 15
Thus, there are 15 two-digit numbers that are divisible by both 2 and 3.
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