How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and…
How many 3-digit natural numbers (without repetition of digits) are there such that each digit is odd and the number is divisible by 5?
8
12
16
24
Solution
All digits are odd and distinct, so digits come from {1, 3, 5, 7, 9}. Divisible by 5 means the units digit is 5. The first two places can be filled from the remaining 4 odd digits in $4 \times 3 = 12$ ways.