perms and combs (1 Viewer)

[qwerla]

I need help with the following:
1) A student writes a random three-digit number using the digits 1-9. what is the probability that the three digits in the number are all the same?
2) five cards are drawn from a standard pack of 52 playing cards (without replacement). what is the probability of drawing at least 3 aces?
thanks!

 

[khabibretiredtoday]

I did this quickly but I think these are the answers
1. Ways to get all 3 digits the same: 9 ways (1+1+1+1+1+1+1+1+1)
Total: 9^3 (9x9x9)
Hence probability = 9/9^3= 1/9^2=1/81
2. Total ways to draw 5 cards from 52 = 52C5
Ways to get at least 3 aces:
Case 1 (3 aces): 4C3*48C2/52C5
Case 2 (4 aces): 4C4*48C1/52C5 = 48C1/52C5
Therefore probability of getting at least 3 aces = (48C1 + 4C3*48C2)/52C5 = 19/10829.