need help with probability

[obsidian stone]

Consider the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Answer each question below.

1. How many three-digit numbers can be formed if repetition is not allowed?
2. How many even three-digit numbers can be formed if repetition is allowed?
3. How many even three-digit numbers can be formed if repetition is not allowed?
4. How many three-digit numbers, with the number 5 as the hundreds digit, can be formed if repetition is not allowed?

Answers:

1. 720
2. 500
3. 360
4. 72

I'm not entirely confident with my answers but could you check when you have some free time to see if they are correct? I would appreciate it

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[obsidian stone]

1st isnt 720

while doint 10P3 you include 0 in first place

which makes it a 2 digit number

you nee to exclude the numbers which begin with 0

.

and even in second one you included 0 in first place

only 9 posibilities to fill first place ur answer is 9*10*5

.

[winter wadi]

(you can do 9\*10*5 which looks like 9*10*5)

[obsidian stone]

oh thanks

[obsidian stone]

4th is ryt
check 3rd one you shouldn't include 0 at first place

[obsidian stone]

1. 9*9*8
2. 9*10*5

[obsidian stone]

ryt

[obsidian stone]

I'm really not sure how to answer number three...

divide it into 2 cases

case 1: put 0 at one's place

case 2: place any other even number other than 0 at ones place

will u try it now

[obsidian stone]

Someone told me about this on the other server. I really have no idea how to do it 🥲

ok see..

case one is i fix 0 at ones place

ways of filling 10th place is 10 ways and filling 100th place is 8ways

so totally 72 posibilities

i think you need to divide in further cases

case 2: ones place is non zero tens place is 0

8*4 =32 ways

case 3: all non zero digits

7*8*4=224 ways

now add them

72+32+224=328

@obsidian stone is it clear

[obsidian stone]

I don't get it tbh...
This is how I got it

Case 1:
Hundreds place: odd
Tens place: odd
9*9*5

Case 2:
Hundreds place: odd/even
Tens place: odd/even
9*9*4

Case 3:
Hundreds place: even
Tens place: even
9*9*3

I had to partially make a tree diagram for me to properly visualize.

[obsidian stone]

well.. what did you do?

[winter wadi]

case 2 seems to overcount?

and which question is this

[obsidian stone]

this question

question 3

[winter wadi]

oh

here’s a tip start counting from the right side

like

[vague scarab]

Ok, not related, but at first I thought you were discussing molecular orbital diagrams 😄

[winter wadi]

how many choices for the last digit, then second

[obsidian stone]

haah

no you generally do that in p and C putting spaces and fill them