Combinatorics: what is the coefficient of (a^2)(b^3)(c) in (2a - b + 3c)^6?

The coefficient of a²b³c is -720

Step-by-step explanation:

Given:

Let 2a-b = x and 3c = y

General term of binomial expansion.

where, n=6 , r=1 ( because exponent of c is 1)

 ----------(1)

Now, we simplify (2a-b)⁵

The exponent of b is 3 and a is 2 .

If we take r=3 will get exponent of b is 3 and a is 2

So, put r=3

Substitute into equation (1)

Hence, The coefficient of a²b³c is -720

answer: two angles are called supplementary if they add up to 180°. example: the two angles (140° and 40°) are supplementary because they add up to 180°.

step-by-step explanation: