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Are all these sentences correct:

a) "On the weekend, there will be a running race."

b) "On the weekend, there will be a bycicle race."

c) "On the weekend, there will be a horse race."

d) "On the weekend, there will be a car(ting) race."

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d) "On the weekend, there will be a car race."
d) "On the weekend, there will be a go-cart race."
d) "On the weekend, there will be a soap box derby. "

Comments  

footrace (US) - foot-race or foot race (UK)

bicycle race (spelling)

horserace or horse race (US) horse-race or horse race (UK)

I don't know what a carting race is.

 AlpheccaStars's reply was promoted to an answer.