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