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

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- Sep 20th 2011, 09:14 PMblackZProbablity 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, 02:50 AMPlatoRe: Probablity Question? Choosing bills?
- Sep 21st 2011, 05:36 AMSorobanRe: 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: $\displaystyle _{10}C_6 \:=\:210$ possible outcomes.

There are: 2 fake and 8 real bills.

We want: 2 fake and 4 real bills.

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

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