probability and combination based questions

I have completed some of the question. I need help with the formulas on how to solve the problems along with making sure what I have done is correct.

5.2 Textbook p 282 Exercises 22, 24, 32

A golf ball is selected at random from a golf bag. If the golf bag contains 9 Titleist's, 8 Maxflis, and 3 Top Flites, find the probability of each event.

22. The golf ball is a Maxfli or Top-Flite
P(E or F) = P(E) + P(F) = P (Maxfli or Top Flite) =P(Maxfli) + P(Top Flite)
n(S)= 9+8+3=20
Probability of finding Maxfli = n(Maxfli)/n(s)= 8/20=2/5
Probability of finding Top Flites= P(Top Flites)= n(Top Flites)/n(s)= 3/20

24. The golf ball is not a Top Flite.
Probability of Top Flite= P(A) n(A)/n/(S) = 3/20
P (E^c)= 1-P(E)
A= 1- 3/20 =17/20
32.

B) 5.3 Selected problems PDF exercises 7 and 19, click here

7.) A bag contains 4 red balls and 6 white balls. Two balls are drawn without replacement.

The number of white balls in the bag = 6. Total number of balls in the bag = 10.
The probability that the first ball is white is 6/10=3/5
After first selection of the balls there are 5 white balls left and 9 balls left this = 5/9
The probability that first ball drawn is white and the second ball drawn is white without replacement is: P(E and F)= P(E) x P(F/E)= 3/5 x 5/9= 1/3

a) What is the probability that the second ball is white, given that the first ball is red?

b) What is the probability that the second ball is red, given that the first ball is white?

c) Answer (a) if the first ball is replace before the second is drawn.

8.) A fair die is rolled. Find the probability that the result is a 4, given that the result is even.

P(4) = 1/6

9.) A fair coin is tossed 3 times. Find the probability of

a) Throwing 3 heads, given that the first toss is head.
P(heads) = ½ P(tails)= ½

b) Throwing 3 heads, given that the first two tosses result in heads.

10.) A fair coin is tossed 14 times. What is the probability of tossing 14 heads, given that the first 13 tosses are heads?

11.) A die is thrown, twice. What is the probability that a 3 will result the first time and a 6 the second time? P(3 the first time)= 1/6 P(6 the second time) = 16 P( 3 the first time and 6 the second time) = 1/6*1/6 = 1/36

12.) A die is rolled and a coin is tossed. What is the probability that the die shows an even number and the coin toss results in a head?
- The sample space S of the experiment described in question 5 is as follows

S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H)
(1,T),(2,T),(3,T),(4,T),(5,T),(6,T)}

- Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows

E={(1,H),(3,H),(5,H)}
- The probability P(E) is given by

P(E) = n(E) / n(S) = 3 / 12 = 1 / 4

19.) A bag contains 9 nickels, 4 dimes, and 5 quarters. If you draw 3 coins at random from the bag, without replacement, what is the probability that you will get a nickel, a quarter, and a nickel, in order?

Instructions: Multiply the two probabilities, type at least two steps in the same Word document

C) 5.5 Textbook pg 313 Exercises 28, 30, 48

28.) List all the permutations of four objects a, b, c, and d, taken two at a time without repetition. What is 4P2?

30.) List all the combinations of four objects a, b, c, and d taken two at a time. What is 4C2?

48.) Forming a committee: Four members from a 20-person committee are to be selected randomly to serve as chairperson, vice chairperson, secretary, and treasurer. The first person selected is the chairperson: The second, vice chairperson, third secretary and fourth the treasure. How many different leadership structures are possible?

nPr=n!/(n-r)! = n=20 r= 4 20P4

20P4= 20!/(20-4)!= 20!/16!= 20 x 19 x 18 x 17 x 16/16=

20 x 19 x 18 x 17 =116,280