noun, na-adjective, noun which may take the genitive case particle 'no'
each of the three is different; three people, three ways
Used when three people each have their own distinct personality, opinion, or approach. Often implies variety or individuality within a group of three.
三人三様の意見が出て、まとまらなかった。
Three different opinions came out, and we couldn't reach an agreement.
彼らは兄弟だけど、性格は三人三様だ。
They are siblings, but each of the three has a completely different personality.
Compound of 三人 (three people) and 三様 (three ways/styles). The exact origin is uncertain, but it follows a common pattern of idiomatic expressions using numbers.