F.3 Maths Question

There are all together 6 banknotes, and there are 6C2 = 15 combinations for 2 random banknote
If T1,T2,T3 mean the $10 notes, B1, B2 mean the $20 notes and F means the $50 note, the 15 ways are
(T1 T2); (T1 T3); (T1 B1); (T1 B2); (T1 F); (T2 T3); (T2 B1); (T2 B2); (T2 F); (T3 B1); (T3 B2); (T3 F); (B1 B2); (B1 F); (B2 F)
Number of ways of having the $50 banknote picked = 2 + 3 = 5
Number of ways of having two $20 banknotes picked = 1
Total probability that the money is sufficient for the dinner = (5 + 1)/15 = 2/5

3.
The only way for paying sufficiently is to pay two $20 dollars bills. there are totally 1+2+3notes in your pocket, and you have totally 6x5=30 ways to draw out different notes. As you just have one way to draw in order to pay sufficiently, so the probavility of you to draw two notes in order to pay sufficiently is 1/30.