Answer: 15
Step-by-step explanation:
(r+1)th term of [tex](a+b)^n[/tex] is given by:-
[tex]T_{r+1}=\ ^nC_r(a)^{n-r}b^r[/tex]
For [tex](a+b)^6[/tex] , n= 6
[tex]T_3=T_{2+1}=\ ^6C_2(a)^{6-2}(b)^2\\\\[/tex]
[tex]=\ \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[/tex]
Hence, the coefficient of the third term in the binomial expansion of [tex](a+b)^6[/tex] is 15.
