If one of the terms in a binomial expansion were 210 P 6 Q 4 , what is the value of N ?
A) 210
B) 6
C) 4
D) 10

Question

Quizplus · Accepted Answer

The term in a binomial expansion follows the formula (a+b)^n where "a" and "b" are the two terms being added, and "n" is the power to which the binomial is being raised. The general term in the binomial expansion is given by the formula nCk * a^(n-k) * b^k, where nCk is the binomial coefficient (also known as "n choose k"), which is the number of ways to choose k elements from a set of n elements. In this case, the term given is 210 P 6 Q 4, which means that a = P, b = Q, k = 4, and nC6 = 210. Therefore, we can solve for n as follows:

nC4 * P^(n-4) * Q^4 = 210 P 6 Q 4
(n*(n-1)*(n-2)*(n-3)/(4*3*2*1)) * P^(n-4) * Q^4 = 210 * P^6 * Q^4
(n*(n-1)*(n-2)*(n-3)/(4*3*2*1)) * P^2 = 210

Simplifying the equation, we get:

(n*(n-1)*(n-2)*(n-3)) = 210 * 4 * 3 * 2

We can see that 210 * 4 * 3 * 2 = 5040, which is equal to 7!, so we can rewrite the equation as:

(n*(n-1)*(n-2)*(n-3)) = 7!

The only value of n that satisfies this equation is n = 10, which means that the answer is D) 10.

If One of the Terms in a Binomial Expansion Were