First, we need to determine how many possibilities there are for the bills in my wallet. There are four bills, and 3 possibilities for each, so the total combinations is 3⁴ = 81.

Consider each case separately

---

Five Dollar Restaurant
The only way I won't have enough money is if all four bills are ones. This can happen in exactly one way, so the probability is

1

81

.

---

Ten Dollar Restaurant
In addition to the possibility described above, the only other way I won't have enough money is if three bills are ones, and one is a five. There are four ways this to happen, so the probability is

1

81

+

4

81

=

5

81

---

Fifteen Dollar Restaurant
In addition to the possibilities above, I won't have enough money if I have a ten and four ones, or 2 ones and 2 fives. The probability then is:

1

243

+

4

81

+

4

81

+

6

81

=

15

81

---

Twenty Dollar Restaurant
In addition to the possibilities above, I won't have enough money if I have 3 fives and a one, or a ten, a five, and 2 ones. So the probability is:

1

81

+

4

81

+

4

81

+

6

81

+

4

81

+

12

81

=

31

81

---

Since each restaurant is equally likely, we divide each probability by four and then add them. This is the probability that I won't have enough money: .

So the probability I will have enough money is:

68

81