In the expansion of (a + b)^6, what is the coefficient of a^2b^4?

In the expansion of (a + b)^6, what is the coefficient of a^2b^4?

Step 1: Identify the expression we are working with, which is (a + b)^6.
Step 2: Recognize that we want to find the coefficient of the term a^2b^4 in the expansion.
Step 3: Use the binomial theorem, which states that (x + y)^n = sum of (nCk * x^(n-k) * y^k) for k from 0 to n.
Step 4: In our case, x = a, y = b, and n = 6.
Step 5: We need to find the term where a is raised to the power of 2 and b is raised to the power of 4.
Step 6: This corresponds to k = 4 because b is raised to the 4th power (and a will then be raised to the 2nd power since 6 - 4 = 2).
Step 7: Calculate the binomial coefficient 6C4, which is the same as 6C2 (since C(n, k) = C(n, n-k)).
Step 8: Use the formula for combinations: nCk = n! / (k! * (n-k)!). Here, 6C2 = 6! / (2! * 4!).
Step 9: Calculate 6! = 720, 2! = 2, and 4! = 24.
Step 10: Substitute these values into the formula: 6C2 = 720 / (2 * 24) = 720 / 48 = 15.
Step 11: Therefore, the coefficient of a^2b^4 in the expansion of (a + b)^6 is 15.

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