Permutations are these not correct?

[rocketboy]

Ok, for some reason my answers for the following 3 questions we were given for homework on permutations are wrong (according to the answers in the back of the text).

I was hoping that somebody could point me in the right direction, these basic ones should be simple for me. Thanks!

In how many ways can 11 players be seated on a bench so that Joey and Jill are not seated next to each other?

arrangements = total arrangements - arrangements where they are together
arrangements = 11! - 10!
arrangements = 36 288 000...text had 32 659 200

In how many ways can four men and four women be seated around a circular table if each man must be flanked by two women?

i arranged the men first, then the women... i said that the first man has 8 possible seats, the second has 3 (because he can't sit beside another man and there has to be room for 2 women beside him) and the third has 2, and the last man has 1 possible seat. This leaves 4 seats for the first women, 3 for the second, 2 for the third, and 1 left for the last women to sit down.

thus, arrangements = (8 x 3 x 2 x 1) + (4!) = 72 text had 144

In how many ways can you form a three-digit number using only the digits of the number 21 150?

well, since it has to be 3 digits, 0 cannot be the first or second.
that leave's 4 digits to be put in the first and second places, and 5 for the last. divide by 2! because of the repeated 1.

thus, arrangements = (4 x 4 x 5) / 2 = 40 ways text has 26

-Jon

 

[QueenFisher]

In how many ways can you form a three-digit number using only the digits of the number 21 150?
well, since it has to be 3 digits, 0 cannot be the first or second.

why can't the second number be 0? isn't 201 a 3-digit number?

 

[Muzza]

arrangements = total arrangements - arrangements where they are together
arrangements = 11! - 10!
arrangements = 36 288 000...text had 32 659 200

11! - 2*10!. Joey can sit to the right or left of Jill.

 

[rocketboy]

Thanks, I should have seen those.

But I still don't get the correct answer for the table question or the digits question.

if we're using the digits from 21 150 to form a 3 digit number...

then in the first spot we can have a 2, 1, or 5
in the second spot we can have a 2, 1, 5, or 0
and in the third spot we can also have a 2, 1, 5, 0

that means we can have 3 x 4 x 4 arrangements = 48 arrangements

but...there are repeats in that so we have to subtract those repeats which are:

if 2 appears in 3 or 2 spots = 3! spots
if 1 appears in 3 or 2 spots = 3! spots
if 5 appears in 3 or 2 spots = 3! spots
if 0 appears in 2 spots, that's 2 spots

so we subtract a total of 6+6+6+2 = 20?

i have to go for dinner...hehe...i will continue trying after.

 

[S&S]

1) Except Joey and Jill, you have 9 other players. Permute these 9 players. The 9 players have 10 possible space between them, then choose 2 out of these 10 space. Then permute Joey and Jill. Multiply all these possibilities:
9!2!(10C2)=as required.

2) For this kind circular sitting problem, you have to fix a people as a reference. I choose fix a man, then other men's position is 3 permute. Between these men you have 4 position for 4 women, then 4 permute:
3!4!= as required.

3) This one is tricky for me. It could be easy if the string we want to for is same length as the original string. But we must form a 3 bit string from a 5 bit string in this question. I don't really know. Can someone help?

 

[S&S]

Here is a computer generated possibility set.

101 125 215 520
102 150 250 521
105 151 251
110 152 501
112 201 502
115 205 510
120 210 511
121 211 512

 

[VietDao29]

In how many ways can you form a three-digit number using only the digits of the number 21 150?
well, since it has to be 3 digits, 0 cannot be the first or second.
that leave's 4 digits to be put in the first and second places, and 5 for the last. divide by 2! because of the repeated 1.
thus, arrangements = (4 x 4 x 5) / 2 = 40 ways text has 26
-Jon

For #3, you can do it a little bit differently from what you did here. First, calculate the total ways to write a 3-digit number with only 2, 1, 5, 0.
That'll be:
3 * 3 * 2 = 18 ways.
This is the number of ways of writing a 3-digit number that has only 1 digit '1' in it.
Then calculate the total way that had 2 digits '1' in it.
* denotes some number chosen randomly from (2, 5, 0)
1*1 = 3 ways.
*11 = 2 ways.
11* = 3 ways.
Now add them together, and see what you get.
Is it clear enough?
Viet Dao,