Question : How many ways are there to choose 3 cells from a 4x4 table such that any two chosen cells do not belong to the same row nor the same column?
What have i done so far :
choosing $1$ from $16$ cells, each giving remaining $9$ cells option, so my equation would be $$(16)(9)(4)=576$$ which my answer was obviously false since $16C3=560$
Please explain where did I go wrong? What shall be the correct approach to this answer?