1. A multi-needle sewing machine, comprising: a plurality of needle bars, each needle bar being configured to receive a needle at a bottom end; a needle bar case in which the plurality of needle bars are disposed in a line and that supports the plurality of the needle bars movably in an up-and-down direction; a needle bar case moving device that, by moving the needle bar case, moves one of the plurality of the needle bars to an image capture position, the image capture position being a position that is located directly above a needle drop position that is a sewing position; and an image capture device that is provided in a position that is lined up with the plurality of the needle bars in the needle bar case, that is positioned in the image capture position by the needle bar case moving device's moving of the needle bar case, and that captures an image, wherein: the image capture device is provided in a position that is to an outside of a group of the plurality of the needle bars that are disposed in the line in the needle bar case, distances between adjacent needle bars of the plurality of the needle bars that are supported by the needle bar case are equal, and a distance between the image capture device and one of the needle bars that is adjacent to the image capture device is an integral multiple of one of the distances between the adjacent needle bars.