Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.

[karspider]

Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.



nCr formula: n!/r!(n-r)!



I've tried everything I can but I don't know how to approach this question.

 

[JimRoo]

Have you tried induction?

You might try (x + y)^1 show that the coefficients are 1 and 1; and then assume it's true for (x+y)^n and show if that is true then it works for the row (x + y) ^(n+1).

I haven't tried that; but it would be my first try.

 

[haruspex]

I would go with JimRoo's first suggestion, induction. You haven't said what definition you have for the terms in Pascal's triangle. I assume it's summing pairs of adjacent entries in one row to generate the next. Use that.