YOU SAID:

but left handed- right people exist

INTO JAPANESE

左左利き右人々 が存在するが、

BACK INTO ENGLISH

Left handed right people exist

INTO JAPANESE

左利きの右人々 が存在します。

BACK INTO ENGLISH

There is a right of left handed people.

INTO JAPANESE

左利きの人々 の権利があります。

BACK INTO ENGLISH

Right handed people.

INTO JAPANESE

右利きの人々。

BACK INTO ENGLISH

Right handed people.