Unsolved flowers problem

This is an extremely difficult sum. My solutions are not correct. So, you can add your own solutions and then the best answer will be chosen.

A gardener keeps 1000 pots in a circle. Each pot has 7 flowers. If he wants to choose 4357 flowers from these lists, and all flowers are identical and rotation is counted only once, then find the ways in which he can choose those flowers. Give the answer in combinatorics form. This is a special challenge and the first person to show me a proper proof will be mentioned below.