1Suppose that 40 cars start at the prestigious vintage car r

1.Suppose that 40 cars start at the prestigious vintage car race that occurs every year in Brownsville, Texas. How many ways can the top 3 cars finish the race?

2.An urn contains 7 red marbles and 3 white marbles. Three marbles are drawn from the urn one after the other. Find the probability that the first two are red and the third is white.

3.There are 10 boys and 15 girls in a class. A certain project has to select 3 boys and 4 girls. How many different possibilities are there?

thank you!

Solution

1)

for the first place : 40 posibilities

for the second place: 39 posibilities

for the 3 place: 38 posibilities

40*39*38= 59,280

2)

At the beginning you have 7 possible red balls out of 10.
P(first red) = 7/10

After that, you have one less red marble (6 red, 3 white)
P(second red) = 6/9

And then you have (5 red, 3 white), but you want the probability the third marble is white.
P(third white) = 3/8

Answer;
7/10 x 6/9 x 3/8
= 126/720
= 7/40
= 0.175

3)

(10C3)* (15C4)=163,800