perms and combs problems i hate (1 Viewer)

[gbong]

yo ppls.... ne help wld b appreciated.

dis question's from understanding series yr 11- pg 300

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1. three identical pens and four identical pencils are arranged in a row.

(a) how many different arrangements are possible? - i got dis one.
7! / (3! x 4!). yeh

(b) if only five writing implememtns are used, how many arrangements are possible?
??????????????

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and

5. eight children consisting of 3 boys and 5 girls are to be seated in a row. in how may ways can this be done if no boys are to be seated next to each other?

for this one, i thought 8! - ( 3! x 6! ), taking the complementary case of the boys seating next to each other but answers says its wrong.

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lastly,

6. how many ways can 3 men and 4 women be arranged in a row with the restrction that arrangements must no be symmetrical, for example WMWMWMW?

agen i took the complementary case. ie 7! - ( 3! x 4! )

yeh dats bout it. thnx guys. meh

 

[Grey Council]

cases cases cases



if only five writing implememtns are used, how many arrangements are possible?
take various cases. possiblities? 2 pencils, 3 pencils, 4 pencils, etc etc. take individual cases, then add

5. eight children consisting of 3 boys and 5 girls are to be seated in a row. in how may ways can this be done if no boys are to be seated next to each other?
cases again.
all possibilities minus (all three sitting next to each other + only two sitting next to each other)

i'll do second in my head, quickly.
8! - (6! + 2.5.5!.7)
i think

 

[coca cola]

2. b) 10 + 10 + 5 = 25. using method described by Grey Council.

5. number of ways is 5!x3!x6C3 = 14400

think like this way. let G represent the girl, therefore:

OGOGOGOGOGO.

where O is the empty slot that the boy can go in. there are 6 slots so 6C3 ways of choosing three slots for the boys. but the boys are all different, i.e. they are not twins or anything, so 3! way of arranging the boys. by the same reasoning there are 5! ways of arranging the girls.

7. your solution is correct, since there are 3!x4! ways of being symmetrical, therefore taking the complementary is correct.

 

[Estel]

I couldn't help compare your thread title to some of these and laugh

"Problems I like to share" - Bill Pender
"Problems I like to share" - Keith Hamann
"Problems I enjoy" - Gus Gale...
"problems i hate " - gbong

Attitude!