The trifecta at most racetracks consists of selecting the first-, second-, and third-place finishers in a particular race in their proper order. If there are nine entries in the trifecta race, how many tickets must you purchase to guarantee a win?

The total tickets to be purchased to guarantee the win =  504 tickets

Step-by-step explanation:

Step 1 :

Number of entries in the trifecta race = 9

The win is to select the first finisher, second finisher and third finisher in their proper order.

We need to find the number of tickets to be purchased to guarantee the win

Step 2 :

Number of ways to select the first finisher = 9

Number of ways to select the second finisher = 8 [the first is selected and fixed. So the number of available finishes is reduced by 1]

Number of ways to select the third finisher = 7

Hence the total tickets to be purchased to guarantee the win = 9 × 8 × 7 = 504

Step 3 :

Answer :

The total tickets to be purchased to guarantee the win =  504 tickets

alright so i think for this one it would to draw it out. this may be hard for me to try and draw, but i will do my best on here:

        r

  /       |     \

notice how it forms 2 triangles inside one bigger triangle.

so if we know the angle spr is the same as psr that is saying the measure of angle p is the same as angle s. this means the big triangle psr is either isosceles or equilateral. in both cases, the triangle is perfectly symmetrical when split down the middle, which is in this case rq. because we know it is perfectly symmetrical on both sides, we know that the two triangles inside the bigger one are equal.