which sentence is correct?

a) They are trying their best in the hope of winning the race.
b) They are trying their best in the hopes of winning the race.
c) They are trying their best in hope of winning the race.
d) They are trying their best in hopes of winning the race.

To determine which sentence is correct, let's analyze each option:

a) "They are trying their best in the hope of winning the race." - This sentence uses the singular form "hope." It suggests that there is a single collective hope shared by the group.

b) "They are trying their best in the hopes of winning the race." - This sentence uses the plural form "hopes." It suggests that each person in the group has their own individual hopes.

c) "They are trying their best in hope of winning the race." - This sentence omits the article "the" before "hope." It sounds somewhat unnatural because "hope" would require an article, such as "in the hope" or "in their hope."

d) "They are trying their best in hopes of winning the race." - This sentence uses the plural form "hopes" like sentence (b). It indicates that each person in the group has their own individual hopes.

Both sentences (b) and (d) are grammatically correct and convey a similar meaning. The choice between them depends on the intended emphasis or style. Sentence (b) focuses on the individual hopes within the group, while sentence (d) emphasizes the collective efforts leading to the shared hopes.

Therefore, the correct options are b) and d).