It's not random if you're forcing it to be uniform. May as well skip the math and do this instead: Divide all the people into groups of 10. Have the members of

It's not random if you're forcing it to be uniform. May as well skip the math and do this instead: Divide all the people into groups of 10. Have the members of a group play each other at whatever, e.g. arm wrestling, to produce a rank from best to worst. Their rank becomes their answer. Now everyone will reply with a number as close to uniform as the total number of people is divisible by the number of choices.