Hello, lax600!

There are: . possible numbers.A three-digit number with no repeated digits is made from the digits 1 through 7.

The last digit must be odd; there are choices: .what is the probability that the number indicated is:

(a) odd

The first two digits are chosen from the remaining 6 digits: . ways.

. . Hence, there are: . odd numbers.

Therefore: .

The last digit must be 5: one choice.(b) A multiple of 5

The first two digits are chosen from the remaining 6 digits: . ways.

. . Hence, there are: . multiples of 5.

Therefore: .

(c) Between 300 and 500

The first digit must be 3 or 4: choices.

The last two are chosen from the remaining 6 digits: . ways.

. . Hence, there are: . numbers between 300 and 500.

Therefore: .

(d) Between 300 and 600

The first digit must be 3, 4, or 5: 3 choices.

The last two digits are chosen from the remaining 6 digits; . ways.

. . Hence, there are: . numbers bewteen 300 and 600.

Therefore: .