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

false

step-by-step explanation:

false.   two legs of the trapezoid would be congruent, but the other two would not.   were all the legs congruent, then we'd have a square; were the 2 shorter sides congruent and the 2 longer sides also congruent, we'd have a rectangle.

$3720

step-by-step explanation:

taxable income = $31000

as per the 2018-2019 us tax bracket, the tax rate is 12% for an individual whose taxable income is between $9,526 to $38,700.

so, the tax to be paid by him = 12% of 31000

= 0.12 * 31000     [12% converted to decimal as 0.12]

= $3720