Probability "at least" question

At an ice cream bar, there are several toppings available. For a large assorted take out order of 16 ice creams, the waitress chose to make 3 strawberry sundae sauce , 5 green sprinkles, 1 chocolate syrup and the rest red sprinkles. It is dark and ice creams are chosen at random. What is the probability that at least one of the first two picked had strawberry sundae sauce?

Thanks for your help.

The easiest way to do problems like this is to determine the probability that no sundae with strawbery sauce was picked amongst the first 2 and then subtract that from 1. So it goes like this:

There are 13 sundaes that are not strawberry. So the probability that you DO NOT pick one in the first 2 picks is:

13/16*12/15 = 156/240 = 13/20

So the probability that AT LEAST 1 is a strawberry sundae is 1 - 13/20 or 7/20.

The other way to do this is to consider the possibilities that at least 1 strawberry sundae is picked. This is done this way

The first is strawberry and the second is not.
The first is not strawberry and the second is.
Both sundaes are strawbery. (Since AT LEAST one of the picks would be strawberry, it does not eliminate the possibility that both are strawberry)

The first probability is 3/16*13/15.
The second is 13/16*3/15.
The last is 3/16*2*15.

Add these up and you get .35 or 7/20.

3/16 x 2/15 = 1/40

Probability = 1/40