Question 12.10E5: Rare Coins Conner Shanahan’s rare coin collection is made up......
Rare Coins
Conner Shanahan’s rare coin collection is made up of 8 silver dollars, 7 quarters, and 5 dimes. Conner plans to sell 8 of his 20 coins to finance part of his college education. If he selects the coins at random, what is the probability that 3 silver dollars, 2 quarters, and 3 dimes are selected?
The number of ways that Conner can select 3 out of 8 silver dollars is _8C_3. The number of ways he can select 2 out of 7 quarters is _7C_2. The number of ways he can select 3 out of 5 dimes is _5C_3. He will select 8 coins from a total of 20 coins. The number of ways he can do so is _{20}C_8. The probability that Conner selects 3 silver dollars, 2 quarters, and 3 dimes is calculated as follows.
= \frac{56 ⋅ 21 ⋅ 10}{125,970} = \frac{11,760}{125,970} = \frac{392}{4199}