Randomly assign an application to 3 reviewers?

If I worked for you then with Sergiomabres's approach I would definitely volunteer to be Reviewer #1. The distribution of applicants between reviewers is distinctly uneven. Reviewer #8 typically gets about four times the applicants that Reviewer #8 gets.
Of course this could be considered a feature - you could make reviewer #8 your most competent or least busy assessor and make interviewer #1 your least able or most busy assessor.

Here is a typical frequency distribution:

s-frequencies.png

Here is an alternate approach that evenly allocates applicants between reviewers. With reference to the attached workbook the 273 combinations of 3 reviewers are located in the range F1:H274. Sergio's approach, for comparison, has been implemented in B1:D274.

There are just 10!/(3!*(10-3)! = 120 combinations of 3 out of 10 reviewers. You have 273 applicants, so twice around the 120 combinations deals with the first 240 applicants. For the remaining 33 applicants if the goal is to maintain an even distribution of applicants among reviewers then we can't just take a block of 33 entries from the combinations table - that would be heavily biased. Instead for each of the last 33 applicants I randomly choose 1 of the possible 120 combinations of 3 reviwers. A constraint here is that we need to make sure to choose all 3 reviewers from the same specific combination without random number recalculation causing us to pick up the three reviewers each from different combinations. This is done by selecting the three column range F242:H242 and then entering as an array formula with CTRL-SHIFT_ENTER:

Formula:

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Copying F242:H242 down to row 274 covers each of the last 33 applications.

Here is a typical frequency distribution resulting from this approach:

g-frequencies.png

In the attached workbook F9 (re-calculate) can be pressed to update both frequency distribution charts.