Question

How many 3-digit numbers are there, with distinct digits, with each digit
odd?

Answer 1

you must have a idea of permutations to do this sum 
the odd numbers are 1,3,5,7,9
1)So putting  1 at hundreds place s the remaining tens and units place can be filled by two numbers from 6 numbers in ⁴P₂ ways = 4 × 3 =  12 ways
2)So putting  3 at hundreds place s the remaining tens and units place can be filled by two numbers from 6 numbers in ⁴P₂ ways = 4 × 3 =  12 ways
3)So putting  5 at hundreds place s the remaining tens and units place can be filled by two numbers from 6 numbers in ⁴P₂ ways = 4 × 3 =  12 ways
4)So putting  7 at hundreds place s the remaining tens and units place can be filled by two numbers from 6 numbers in ⁴P₂ ways = 4 × 3 =  12 ways
5)So putting  9 at hundreds place s the remaining tens and units place can be filled by two numbers from 6 numbers in ⁴P₂ ways = 4 × 3 =  12 ways
so adding 12 +12 +12 +12 +12 = 60 ways 

Answer 2

we have ( 1,3,5,7,9)

first digit already used in hundred place

second dight used

then we have 5*3*4=60