Explain why the rows of pascal’s triangle are symmetric. that is, explain why c(n, k) = c(n, (n − k))

The rows of Pascal’s triangle are symmetric.

Step-by-step explanation:

Each row of Pascal's triangle is symmetric.

Clearly

nCr=nCn-r

since choosing r objects from n objects leaves n−r objects, and choosing n−r objects leaves r objects. This means that the coefficient of in the expansion of is the same as the coefficient of .

Let Y be the number of compact cars and 20 - Y be the number of full-sized car. If the total cost of 20 cars is $372, 000. Then we have: (Cost of compact car * number of compact car)+ (cost of full-sized car * number of full-sized car). So we have (15, 000 * Y) + (23, 000 * (20 -Y)) = 372, 000. Multiplying the expression, we have; 15, 000Y + 460, 000 - 23000Y = 372, 000. 15000Y - 23000Y = 372, 000 - 460, 000. -8000Y = - 88, 000. Hence Y = 11. Hence 11 compact cars were bought.