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y=2x+20; x is any integer greater than or equal to 0, and y is an integer greater than or equal to 20.
Answer: 15
Step-by-step explanation:
(r+1)th term of
is given by:-

For
, n= 6

![=\ \dfrac{6!}{4!2!}a^4b^2\ \ \ [^nC_r=\dfrac{n!}{r!(n-r)!}]\\\\=\dfrac{6\times5\times4!}{4!\times2}a^4b^2\\\\=3\times5a^4b^2\\\\ =15a^4b^2](https://tex.z-dn.net/?f=%3D%5C%20%5Cdfrac%7B6%21%7D%7B4%212%21%7Da%5E4b%5E2%5C%20%5C%20%5C%20%5B%5EnC_r%3D%5Cdfrac%7Bn%21%7D%7Br%21%28n-r%29%21%7D%5D%5C%5C%5C%5C%3D%5Cdfrac%7B6%5Ctimes5%5Ctimes4%21%7D%7B4%21%5Ctimes2%7Da%5E4b%5E2%5C%5C%5C%5C%3D3%5Ctimes5a%5E4b%5E2%5C%5C%5C%5C%20%3D15a%5E4b%5E2)
Hence, the coefficient of the third term in the binomial expansion of
is 15.