Question

1. You are playing poker and are dealt 7 cards (without replacement) from a standard 52 card deck. How many 7-card poker hands are possible? (Hint: order doesn’t matter in poker, just the hand you are dealt).

a.)52P7 = 6.74E11 (Same as 6.74x 10¹¹)

b.)52C7 = 133,784,560

c.)52!    = 8.0658E67

d.)7x52 = 3640

2.)Outside of a home, there is a keypad that can be used to open the garage door if the correct four digit code is entered. The key pad has 10 digits (0 thru 9 ) on it. How many codes are possible?

a.)10! = 3,628,800

b.)10x10x10x10 = 10,000

c.)10C4 = 210

d.)10P4 = 5,040

3.)Assume you have an .mp3 player with 50 of your favorite songs on it. You can only select 10 of these songs for a party and the order of the songs is important. How many ways can you select 10 songs to play?

a.)50! = 3.041E64

b.)10x10x10x10 = 10,000

c.)50C10 = 1.027E10

d.)50P10 = 3.727E16

3.)You have a drawer filled with 16 socks: 8 black socks and 8 white socks, but they are not matched up and are just lying in the drawer. It is dark and you reach into the drawer and pull out 2 socks at random. What is the probability you have a matched pair of socks. (Hint: use a tree diagram)

a.)0

b.).233

c.).467

d.).5

4.)You toss a fair coin three times and observe the number of heads. What is the probability of getting exactly two heads? (Hint: use a tree diagram).

a.).125

b.).25

c.).375

d.).5

Answer 1

Here' the answer to the question with full concept. Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

1. Selecting 7 cards from 52 in any order can be done in 52C7 ways. We use C and not P

when in order of picking is not important

b. is correct

2. Number of codes possible is 10*10*10*10 = 10^4.

b. is correct

3. Since order of selection is important we can do in 50P10 ways.

d. is correct

4. P(match) = P(both are white)+P(both are black) = 2*8C2/(16c2) = (2*8*7/2)/(16*15/2) = .467

5. toss coin 3 times and observe number of heads.

P(exactly 2 heads) = 3C2 *(1/2)^2 (1/2)^1 = 3/8 = .375

c. is correct