A 3-digit number is formed from the digits 1,23,4,5,6,7and 8 without repatition. How many numbers formed are odd?

Without restriction, to get a 3-digit number from the 8 digits without repetition, there are 8 choices for the hundreds digit, 7 choices for the tens digit, and 6 choices for the units digits.
Number of permutation to get a 3-digit number without restriction
= 8 × 7 × 6

To get a 3-digit odd number from the 8 digits, there are 4 choices for the units digit, 7 choices for the hundreds digit, and 6 choices for the tens digits.
Number of permutation to get a 3-digit odd number
= 4 × 7 × 6

P(the 3-digit number formed is odd)
= (4 × 7 × 6) / (8 × 7 × 6)
= 1/2