pkw209 wrote:A bag contains 3 gold coins and 7 silver coins. The bag contains nothing else. If 3 coins are selected at random and without replacement from the bag, what is the probability that exactly 2 of the coins are silver?
A) 7/40
B) 7/24
C) 3/10
D) 21/40
E) 2/3
The number of ways to select 2 silver coins is 7C2 = (7 x 6)/2! = 21.
The number of ways to select 1 gold coin is 3C1 =3.
The number of ways to select 3 coins is 10C3 = (10 x 9 x 8)/3! = (10 x 9 x 8)/(3 x 2 x 1) = 10 x 3 x 4 = 120.
So the probability is (21 x 3)/120 = 63/120 = 21/40.
Alternate Solution:
There are 3 different ways to select exactly 2 silver and 1 gold coin, without replacement, out of the coins in the bag. The outcomes are: (GSS) or (SGS) or (SSG).
The probability of GSS is 3/10 x 7/9 x 6/8 = 21/120.
The probability of SGS is 7/10 x 3/9 x 6/8 = 21/120.
The probability of SSG is 7/10 x 6/9 x 3/8 = 21/120.
Thus, the probability of drawing exactly 2 silver and 1 gold coin is 21/120 x 3 = 63/120 = 21/40.
Answer: D
