How many 3-digit numbers are there, with distinct digits, with each digit odd?
Guadara0c2x
Answered question
2023-02-25
How many 3-digit numbers are there, with distinct digits, with each digit odd?
Answer & Explanation
Saugers5vf
Beginner2023-02-26Added 6 answers
The odd digits are I, 3, 5, 7, 9 . ∴ 5 is the total amount of odd digits.
The hundred's place can obviously be filled with any of the following five digits: 1, 3, 5, 7, or 9.
There are thus 5 options for taking the place of the hundred.
Now, 4 digits are left. So, ten's place can be filled with any of the remaining 4 digits in 4 ways.
Now, the unit's place can be filled with in any of the remaining 3 digits. So, there are 3 ways of filling the unit's place.
Hence, the total number of required number = 5×4×3=60
The hundred's place can obviously be filled with any of the following five digits: 1, 3, 5, 7, or 9.
There are thus 5 options for taking the place of the hundred.
Now, 4 digits are left. So, ten's place can be filled with any of the remaining 4 digits in 4 ways.
Now, the unit's place can be filled with in any of the remaining 3 digits. So, there are 3 ways of filling the unit's place.
Hence, the total number of required number = 5×4×3=60
