[SPLIT] how many 5-card hands have at least two red cards?

[Guest]

The game of euchre uses only the 9s, 10s, jacks, queens, kings, and aces from a standard deck of cards. How many five hand cards have AT LEAST two red cards?

How should I do the computations for AT LEAST however much of something?

Thank you1

 

[pka]

You have 20 cards in all, half are black.
\(\displaystyle {10 \choose 5}\) ways to have no red cards.
\(\displaystyle {10 \choose 1}{10 \choose 4}\) ways to have exactly one red.
Add those up and substract from the total \(\displaystyle {20 \choose 5}\) that will tell us how many ways to have at least two red cards.