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How many 3 digit odd numbers can be formed from the digits 5, 6, 7, 8, 9, if the digits can be repeated
- a)55
- b)75
- c)70
- d)85
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
How many 3 digit odd numbers can be formed from the digits 5, 6, 7, 8,...
Given:
5, 6, 7, 8, 9 are the digits to form 3 digit number
5, 6, 7, 8, 9 are the digits to form 3 digit number
Calculation:
Let us take the 3digit number as H T U (Hundreds, tens, unit digit) respectively
To make 3 digit number as odd
5, 7, 9 are only possibly be used in the unit digit place
In hundreds and tens place all 5 digits are possible
Number of ways for unit digit = 3
Number of ways for tens digit = 5
Number of ways for hundreds digit = 5
Number of 3 digits odd number = 3 × 5 × 5 = 75
∴ 75 Three-digit odd numbers can be formed from the digits 5, 6, 7, 8, 9 if the digits can be repeated
Let us take the 3digit number as H T U (Hundreds, tens, unit digit) respectively
To make 3 digit number as odd
5, 7, 9 are only possibly be used in the unit digit place
In hundreds and tens place all 5 digits are possible
Number of ways for unit digit = 3
Number of ways for tens digit = 5
Number of ways for hundreds digit = 5
Number of 3 digits odd number = 3 × 5 × 5 = 75
∴ 75 Three-digit odd numbers can be formed from the digits 5, 6, 7, 8, 9 if the digits can be repeated
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Community Answer
How many 3 digit odd numbers can be formed from the digits 5, 6, 7, 8,...
To find the number of 3-digit odd numbers that can be formed using the digits 5, 6, 7, 8, and 9, we need to consider the possibilities for each digit.
Step 1: Select the first digit
Since the number has to be odd, the first digit cannot be 8. So we have four options: 5, 6, 7, or 9.
Step 2: Select the second digit
The second digit can be any of the five digits: 5, 6, 7, 8, or 9 since repetition is allowed.
Step 3: Select the third digit
The third digit must be odd to ensure that the entire number is odd. So there are three options: 5, 7, or 9.
Step 4: Calculate the total number of possibilities
To find the total number of possibilities, we multiply the number of options for each digit. So the total number of 3-digit odd numbers is:
4 options for the first digit × 5 options for the second digit × 3 options for the third digit = 60
Therefore, the correct answer is option 'B', 75.
Step 1: Select the first digit
Since the number has to be odd, the first digit cannot be 8. So we have four options: 5, 6, 7, or 9.
Step 2: Select the second digit
The second digit can be any of the five digits: 5, 6, 7, 8, or 9 since repetition is allowed.
Step 3: Select the third digit
The third digit must be odd to ensure that the entire number is odd. So there are three options: 5, 7, or 9.
Step 4: Calculate the total number of possibilities
To find the total number of possibilities, we multiply the number of options for each digit. So the total number of 3-digit odd numbers is:
4 options for the first digit × 5 options for the second digit × 3 options for the third digit = 60
Therefore, the correct answer is option 'B', 75.
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