1980 AHSME Problems/Problem 20
Problem
A box contains pennies,
nickels, and
dimes. Six coins are drawn without replacement,
with each coin having an equal probability of being chosen. What is the probability that the value of coins drawn is at least
cents?
Solution 1
We want the number of Successful Outcomes over the number of Total Outcomes. We want to calculate the total outcomes first. Since we have coins and we need to choose
, we have
=
Total outcomes. For our successful outcomes, we can have
penny and
dimes,
nickels and
dimes,
nickel and
dimes, or
dimes.
For the case of penny and
dimes, there are
ways to choose the dimes and
ways to choose the pennies. That is
successful outcomes. For the case of
nickels and
dimes, we have
ways to choose the dimes and
ways to choose the nickels. We have
=
successful outcomes. For the case of
nickel and
dimes, we have
. Lastly, we have
dimes and
nickels and
pennies, so we only have one case. Therefore, we have
=
See also
1980 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 19 |
Followed by Problem 21 | |
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