Aroom contains 8 people, each of a different age. the people leave the room in random order, one at a time. what is the probability that they leave the room in ascending order of their ages (youngest to oldest)? the probability that they leave the room in ascending order of their ages is nothing.

2.48 × 10⁻⁵

Step-by-step explanation:

Number of people in the room of a different age = 8 people

The number of ways people can leave the room  = 8!

                                                                                 = 40320

They leave the room in ascending order is  = 1 way

The probability they leave the room in ascending order of their ages =

= 2.48 × 10⁻⁵

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.

n

step-by-step explanation: