Probabilities!!! HELP MEEEE!!!?

Question

How many license plates with three numbers followed by three letters can be created if the letter 'O' and number '0' cannot be used?

How many ways could 8 people be lined up?

A 20-sided die (numbered 1 through 20) is tossed twice. What is the probability that both rolls will land on a prime number?

Answer 1

25*24*23*9! = 5,007,744,000

8! = 40320

Primes are 2,3 5 7,11,13 17,19 =total of 8.
So P = 8/20*8/20 = .16

Answer 2

1.three letters followed by 3 numbers without using O or 0. There are 25 letters without O and there are 9 numbers without 0.
There are 25 ways to choose each of the 3 letters and 9 ways to choose each of the 3 numbers.
25*25*25*9*9*9=11390625


2. There are 8 ways to choose the first person, 7 ways to choose the second, 6 ways to choose the third...
so 8*7*6*5*4*3*2*1=8!=40320

3. What are the primes less then 20? 2,3,5,7,11,13,17,19
So there are 8 primes less then 20. So the probability of rolling a prime is 8/20 so the probability of that happening twice is (8/20)*(8/20)=(2/5)*(2/5)= 4/25=16%

Answer 3

To calculate probablilities you have to count the number of options.
lets look at the liscence plate problem.
If 0 an O cannot be used then there are 25 letters and 9 numbers. Since we can reuse letters and numbers (a plate could be 112 ABB) we dont have to worry about which numbers and letters are used.
Lets look at the first 2 numbers in the liscence plate.
You have 9 options for the first one. There are 9 options to go with each of the first 9 options. Therefore you have 9x9 options on the first two numbers.
The number of liscence plates would be 9x9x9x25x25x25

The 8 people problem is different. Now we are talking about all the same people in different orders. You have 8 options for the first positions, 7 for the second, etc. So the number of orders are 8x7x6x5x4x3x2x1.

The third one we are looking are the probablility of a specific number coming up. There are 8 prime numbers on each die (1,2,3, 7,11,13,17, 19) that means for your first die you have 8 out of 20 chances or 20/8 or 0.40. Your second die has the same. So your probablility is (20/8)*(20/8) = 0.16 = 16%

Answer 4

I would probably screw this question up, but I guess a try would be fine =D.

1. 25*25*25*9*9*9 = 11,390,625

2. Way 8 people can line up: 8! = 40,320

3. 20*20 = possible choices. possible choices = 400.

There are 8 prime numbers in from 1 to 20. 8*8=64

64/400 is the probability.

I think I got the third one wrong so check it.

Answer 5

There are nine digits and 25 letters available.
9 x 9 x 9 x 25 x 25 x25 = 11390625

8!=40320

There are (2,3,5,7,11,13,17,19) 8 primes so at each roll the probability of a prime is 8/20=2/5
The probability of 2 primes in 2 rolls is 2/5 x 2/5 = 4/25

Answer 6

license plate, let
N1 = first number
N2 = 2nd number
N3 = 3rd number
L1 = 1st letter
L2 = 2nd letter
L3 = 3rd letter
then
license plate = N1 N2 N3 L1 L2 L3

There are 9 choices for N1 (1,2, ...,9)
There are 9 choices for N2 (1,2, ...,9)
There are 9 choices for N3 (1,2, ...,9)
There are 25 choices for L1 (A-N, P-Z)
There are 25 choices for L2 (A-N, P-Z)
There are 25 choices for L3 (A-N, P-Z)

number of possible license plates =
9 * 9 * 9 * 25 *25 * 25 =11390625


line-up problem
LineUp = P1 P2 P3 P4 P5 P6 P7 P8
there are 8 choices for person 1
7 choices for person2
6 choices for person 3, etc....
...
1 choices for person 8
# of ways to line up 8 persons is
8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 = 40320 ways

Answer 7

license plates: 9^3*25^3
line of people: 8!
prime die: (8*8)/(20*20)

Answer 8

plates ?
people ?
dice ?

Who cares? I haven't slept in two days and didn't get on here to think, just to relax.

Answer 9

ask a math teacher