Consider the following game: a drum contains 10 balls, each numbered from 1 to 10. three balls are randomly drawn, without replacement, from the drum. prior to the draw, you fill out a card by selecting three numbers from 1 to 10. to win a prize, the numbers you select have to correspond to the numbers of the balls drawn, in any order. what is the probability of winning a prize?

1/120

Step-by-step explanation: First to calculate the probability, we must know the possible number of way that 3 balls can be drawn from 10 balls numbered 1-10, and the number of ways that the 3 numbers selected from the player will match the number the numbers that the player chose.

To get the total number of outcomes this entails 10C3

From the formula nCr = n!/(r!(n-r)!)

10C3= 10!/(3!(10-3)!)

10! = 10*9*8*7*6*5*4*3*2*1 = 3628800

3! = 3*2*1 = 6

(10-3)! = 7! = 7*6*5*4*3*2*1 = 5040

10C3 = 3628800/(6*5040) = 120

Of all the 120 outcomes possible, only one outcome is expected to match all the 3 numbers that the player had written down, hence the probability for winning the draw will be

3C3/10C3

=1/120 = 0.0083333333333

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3