# Probablity Question? Choosing bills?

• Sep 20th 2011, 10:14 PM
blackZ
Probablity Question? Choosing bills?
Out of 10 $20 bills, 2 are counterfeit, 6 bills are chosen at random. What is the probability that both counterfeit bills are chosen? --my attempt-- C(10,6)/(C(6,2) *C(10,2)) Is this correct? I am not sure. Thanks • Sep 21st 2011, 03:50 AM Plato Re: Probablity Question? Choosing bills? Quote: Originally Posted by blackZ Out of 10$20 bills, 2 are counterfeit, 6 bills are chosen at random. What is the probability that both counterfeit bills are chosen?

Standard notation is $\binom{n}{k}=\frac{n!}{k!(n-k)!}$, n things choosing k.

So the answer will be $\frac{\dbinom{8}{4}}{\dbinom{10}{6}}$.
• Sep 21st 2011, 06:36 AM
Soroban
Re: Probablity Question? Choosing bills?
Hello, blackZ!

Quote:

Out of ten \$20 bills, two are counterfeit.
Six bills are chosen at random.
What is the probability that both counterfeit bills are chosen?

There are: $_{10}C_6 \:=\:210$ possible outcomes.

There are: 2 fake and 8 real bills.
We want: 2 fake and 4 real bills.

There are: . $(_2C_2)(_8C_4) \:=\:1\cdot70 \:=\:70$ ways.

$P(\text{2 fake, 4 real}) \:=\:\frac{70}{210} \:=\:\frac{1}{3}$