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I need a little help with how to go about proving the following:

the formula for n choose k is n!/(k!(n-k)!)

For this, I have proceeded as follows:

Base case P(j):

I am not sure if this is correct... but the next step would be to Assume P(k), I get stuck at that step because the algebraic expression does not look right... Am I going about this the right way? Thanks.