Definition from macmillandictionary.com
The whole team was counting on me, and I let them down.
You can always count on him for good advice.
I knew I could count on you to be on time.
I was counting on Jane driving me home.
You can always count on Ted to make a mess of the cooking.
Tournament directors are counting on good weather.
We’re counting on about 20 people coming to the meal.
She hadn’t counted on it raining.