Using the set {1,3,6,7,8,9} how many odd numbers can we construct between 100-999, if no element may be used more than once in a number

Odd numbers end with 1 or 3 or 5 or 7 or 9

alrighty, the last number can be 1 or 3 or 7 or 9 (we aren't given 5 in the set)

4 choices for the last number

for the other 2 numbers, we can use any other numbers

6 numbers in the set

6 choices for the first digit

5 for the 2nd

4 for the 3rd digit

so there are 6*5*4 or 120 different odd numbers that can be constructed withthe given numbers in the set