If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what

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Question: If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what does C(n,k) represent?

Options:

Correct Answer: The number of ways to choose k items from n.

Solution:

C(n,k) represents the number of ways to choose k items from n, which corresponds to the coefficient of x^k.

If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what does C(n,k) represent?

If the coefficient of x^k in the expansion of (x + 1)^n is given by C(n,k), what does C(n,k) represent?

Step 1: Understand that (x + 1)^n is a mathematical expression that can be expanded using the binomial theorem.
Step 2: The binomial theorem states that (a + b)^n can be expanded into a sum of terms involving coefficients.
Step 3: In the expression (x + 1)^n, 'x' is one part (a) and '1' is the other part (b).
Step 4: The expansion will have terms like x^k, where k can be any number from 0 to n.
Step 5: The coefficient of x^k in this expansion is represented by C(n, k).
Step 6: C(n, k) is a mathematical notation that represents the number of ways to choose k items from a total of n items.
Step 7: Therefore, C(n, k) not only gives the coefficient of x^k but also tells us how many different combinations of k items can be selected from n.

Binomial Coefficient – C(n,k) represents the number of ways to choose k items from a set of n items, which is also the coefficient of x^k in the binomial expansion of (x + 1)^n.