i need help with this question their are 3 of the i don't get help plz?

Question

Tamara has found 10 websites to research for her project. In how many ways can she visit half of the websites?

How many 4-digit codes can be created if no digit can be repeated?

A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a marble at random without looking. Find the probability of each event. Write your answer as a fraction in simplest form: P(blue or purple)

Answer 1

The first one is 10 P 5

10!
------
(10 - 5)!

10!
----- = 10*9*8*7*6 = 30240
5!



4 digit codes.
0-9 = 10 for the first
9 for the second
8 for the third
7 for the forth
-------------
10 x 9 x 8 x 7 = 5040




20 marbles total, P (blue or purple)
So 8 blue and purple,

8/20 = 2/5

Answer 2

1. Tamara has found 10 websites to research for her project. In how many ways can she visit half of the websites?

Ans: All you need to find is to find the number of possible permutations.

So the answer is:
10P5 = 10!/(10-5)! = 10!/5! = 10*9*8*7*6 = 30240 ways.

2. How many 4-digit codes can be created if no digit can be repeated?

Assuming you have to use only numbers from 0-9, then you have 10 different possible numbers for the 1st digit. Since one of them is used in the 1st digit, you have 9 numbers to chose from for the 2nd digit. Likewise you have 8 numbers to chose from for the 3rd digit and 7 numbers for the 4th. So totally you have 10*9*8*7 = 5040 different codes. If you generalize, then the number of 4 digit codes available if you are allowed to use n characters is given by: (n-3)*(n-2)*(n-1)*n

3. A jar contains 5 blue marbles, 8 red marbles, 4 white marbles, and 3 purple marbles. Suppose you pick a marble at random without looking. Find the probability of each event. Write your answer as a fraction in simplest form: P(blue or purple)

There are 5+8+4+3 marbles = 20 marbles.

Probability of picking a blue marble = 5/20 = 1/4
Probability of picking a red marble = 8/20 = 2/5
Probability of picking a white marble = 4/20 = 1/5
Probability of picking a purple marble = 3/20

Therefore Probability of picking a blue or purple marble = 5/20 + 3/20 = 8/20 = 2/5 = 0.4

Answer 3

2) (I am assuming you work in base ten, where the 10 digits are 0, 1, 2, ... ,8, 9)
The first digit can be any of 10 (10 ways)
Once the first digit is fixed, the second digit can be any of the remaining 9. (total 10*9 ways to have 2 digits)
The first two are picked, then the third can be any of the remaining 8: 10*9*8 = 720 possible combinations
By now, you see the trend.

I have assumed that there are no restrictions (e.g., in my example, the first digit can be 0).

---
There are 20 marbles:
Pick one marble.
P(blue) = 5/20 = 1/4
P(blue or red) = (5+8)/20
P(blue or red or white) = (5+8+4)/20
P(blue or red or white) = 1 - P(purple) = 1 - 3/20 = 20/20 - 3/20 = 17/20
and so on.
(don't forget to simplify the fractions, e.g., 12/20 = 6/10 = 3/5)

Answer 4

1)
10 possibilites for the first visit, 9 possibilities for the second, etc. So the result is 10 * 9 * 8 * 7 * 6 = 30240 ways.

2)
Similar question to the previous one. The result is 10 * 9 * 8 * 7 = 5040 codes.

3)
P(blue or purple) = ( 5 + 3) / (5 + 8 + 4 + 3 ) = 8 / 20 = 0.4
(40 percent)

Answer 5

Sounds like permutations and combinations!
1st question...not quite sure what they're asking.
2nd question...10 x 9 x 8 x 7 = 5040 (if 0 is used as a number)
3rd...blue 5/20 or 1/4....purple 3/20

Answer 6

Divide the number of marbles of any color by the total number of marbles. This is the probability. Multiple this result to get the probability expressed as a percentage.

Answer 7

9000 codes

as for the marbles
5/20=1/4
8/20=2/5
4/20=1/5
3/20=3/20

Answer 8

1) 30240

2) 24

3) blue: 1/4
red: 2/5
white: 1/5
purple: 3/20