what is the coefficient of the third term in the binomial expansion of (a + b)^6?\n1\n15\n20\n90

Explanation:

Step1: Recall binomial theorem formula

The binomial expansion of $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, where $\binom{n}{k}=\frac{n!}{k!(n - k)!}$.

Step2: Determine the value of k for the third - term

For the binomial expansion, the terms are numbered starting from $k = 0$. So for the third - term, $k=2$ and $n = 6$.

Step3: Calculate the binomial coefficient

$\binom{6}{2}=\frac{6!}{2!(6 - 2)!}=\frac{6!}{2!4!}=\frac{6\times5\times4!}{2\times1\times4!}=15$.

Answer:

15