I have a bag that contains 6 nickels and 5 pennies. I draw coins from the bag at random, without replacement. Find the probability that after drawing 4 coins, I have removed at most 2 pennies from the bag.
Since you have at most 2 pennies, you can have 0 pennies, 1 penny, or 2 pennies.
The number of ways to select 0 pennies and 4 nickels: 5C0 · 6C4
The number of ways to select 1 penny and 3 nickels: 5C1 · 6C3
The number of ways to select 2 pennies and 2 nickels: 5C2 · 6C2
Add those three answers to together and divide by the number of ways to select 4 coins from 11 coins:
The number of ways to select 4 coins from 11 coins: 11C4
Since you have at most 2 pennies, you can have 0 pennies, 1 penny, or 2 pennies.
The number of ways to select 0 pennies and 4 nickels: 5C0 · 6C4
The number of ways to select 1 penny and 3 nickels: 5C1 · 6C3
The number of ways to select 2 pennies and 2 nickels: 5C2 · 6C2
Add those three answers to together and divide by the number of ways to select 4 coins from 11 coins:
The number of ways to select 4 coins from 11 coins: 11C4