Problem #PRU-5239

Problem

Jamie’s drawer is pretty big. It has infinitely many crayons. In fact, for every colour of crayon, there are infinitely many crayons of that colour.
In every group of $9$ randomly chosen crayons from Jamie’s drawer, some $3$ will have the same colour. Jamie chooses $25$ crayons at random. Prove that some $7$ of them will have the same colour.