1. ## Probability

A three digit numberal with no repeated digits is made from the digits 1 throguh 7. What is the probability that the number indicated is:

odd:

7*6*4

A multiple of 5:

7*6*1

Between 300 and 500

2*6*5

Between 300 and 600

4*5*5

thats what i think it is but I doubt they're right so could anyone help me please?

2. Hello, lax600!

A three-digit number with no repeated digits is made from the digits 1 through 7.
There are: .$\displaystyle 7\!\cdot\!6\!\cdot\!5\:=\:210$ possible numbers.

what is the probability that the number indicated is:
(a) odd
The last digit must be odd; there are $\displaystyle {\color{blue}4}$ choices: .$\displaystyle \{1,3,5,7\}$
The first two digits are chosen from the remaining 6 digits: .$\displaystyle 6\!\cdot\!5\:=\:{\color{blue}30}$ ways.
. . Hence, there are: .$\displaystyle 4 \times 30 \:=\:120$ odd numbers.

Therefore: .$\displaystyle P(\text{odd}) \;=\;\frac{120}{210}\;=\;\boxed{\frac{4}{7}}$

(b) A multiple of 5
The last digit must be 5: one choice.
The first two digits are chosen from the remaining 6 digits: .$\displaystyle 6\!\cdot\!5\:=\:{\color{blue}30}$ ways.
. . Hence, there are: .$\displaystyle 1\!\cdot\!30\:=\:30$ multiples of 5.

Therefore: .$\displaystyle P(\text{multiple of 5}) \;=\;\frac{30}{210} \;=\;\boxed{\frac{1}{7}}$

(c) Between 300 and 500

The first digit must be 3 or 4: $\displaystyle {\color{blue}2}$ choices.
The last two are chosen from the remaining 6 digits: .$\displaystyle 6\!\cdot\!5\:=\:{\color{blue}30}$ ways.
. . Hence, there are: .$\displaystyle 2\!\cdot\!30 \:=\:60$ numbers between 300 and 500.

Therefore: .$\displaystyle P(\text{between 300 and 500}) \;=\;\frac{60}{210} \;=\;\boxed{\frac{2}{7}}$

(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; .$\displaystyle 6\!\cdot\!5\:=\:{\color{blue}30}$ ways.
. . Hence, there are: .$\displaystyle 3\!\cdot\!30 \:=\:90$ numbers bewteen 300 and 600.

Therefore: .$\displaystyle P(\text{between 300 and 6 00}) \:=\;\frac{90}{210} \;=\;\boxed{\frac{3}{7}}$

3. t ty