There are 6 people in a raffle drawing, two raffle winners each win gift cards,
each gift card is the same. how many ways are there to choose the winners?
decide if the situation involves a permutation or a combination, and then find
the number of ways to choose the winners.

B. Combination: Number of ways = 15

Step-by-step explanation:

2 winners are to be chosen out of 6 people participating in the raffle drawing. In this case the order of selection does not matter, therefore, this situation involves combinations

So, we have to find combinations of 6 people taken 2 at a time. This can be represented by 6C2. The general formula for combinations is:

In this case n = 6 and r = 2. Using these values, we get:

Thus, there are 15 ways to chose the winners. So, option B gives the correct answer.

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.