# Math Help - 3 numbers picked from 1 - 10 prob lowest no is 5

1. ## 3 numbers picked from 1 - 10 prob lowest no is 5

I have the question you have the numbers 1 - 10 and 3 numbers are picked at random whats the probability the lowest picked number is 5

What i guessed it would be is to use the choose functions so 10C1 * 4C1 * 3C1 / 10C3 which equals 1 which is wrong. But ive no idea how else to do it.

2. Hello, renlok!

You have the numbers 1 - 10 and three numbers are picked at random.
What's the probability the lowest picked number is 5?
Choosing three numbers from ten numbers, there are: . $_{10}C_3 \:=\:{10\choose3} \:=\:120$ outcomes.

We want the "5" and two Others.
The two Others are chosen from {6, 7, 8, 9, 10}.
.There are: . $_5C_2 \:=\:{5\choose2} \:=\:10$ ways.

Therefore: . $P(\text{lowest is 5}) \;=\;\frac{10}{120} \;=\;\frac{1}{12}$