Question

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?

(a) 3

(b) 4

(c) 5

(d) 6

Answer 1

To construct odd numbers between 100 and 999 using the given set, we need to consider all possible combinations of the digits. There are 6 odd numbers with all odd digits and 18 odd numbers with one even digit.

Step-by-step explanation:

To construct odd numbers between 100 and 999 using the set {1, 3, 6, 7, 8, 9}, we need to consider all possible combinations of these digits without repetition.

Since we need to construct a three-digit number, the first digit cannot be 0. The only odd digit available is 1, so we have two cases to consider:

Case 1: The two remaining digits are also odd. There are 3 odd digits available, so the number of possible numbers in this case is 3 * 2 * 1 = 6.

Case 2: One of the remaining digits is even. There are 3 odd digits and 3 even digits available, so the number of possible numbers in this case is 3 * 3 * 2 = 18.

Therefore, the total number of odd numbers that can be constructed is 6 + 18 = 24.