Dealing with probability with a bag of coins:

Question

Assume that you select 5 coins at random from 10 coins: 6 dimes and 4 quarters.
What is the probability that all of the coins selected are dimes? Enter your answer as a fraction.

Answer 1

You could also do this as ₆C₅/₁₀C₅ = 1/42

Answer 2

Do you replace the coins after each draw or not? I have a hunch that it's the latter. If so, here's my approach:

 

In the first pick, you have 6 dimes and 10 coins, so the odds of getting a dime is 6/10.

In the second pick, assuming you already picked a dime, you have 5 dimes and 9 coins, so the odds of getting a dime are 5/9.

Continue like this for the other three picks to get

 

(6/10) * (5/9) * (4/8) * (3/7) * (2/6) = 0.0238 = 2.38%

Answer 3

The probability of selecting a dime on the first pick is 6/10, on the second pick 5/9, and so forth.

 

Total: 6/10 x 5/9 x 4/8 x 3/7 x 2/6 = 1/42