IIT JEE , AIEEE Forum - Mathematics , Algebra

saurabh_reincarnated

there r 12 flowers of one type and 3 flowers of other type.

in how many ways can they be arranged to form a garland...

m.viddya

the total no. of flowers will be 15.

The number of circular permutations of n things taken ll at a time in one direction is 1/2(n-1)!

therefore,

it is 14!/2.

bitti_friend

the 3 flowers of one type can be assigned 3 pos among the 15 in
((15)C3)/3! ways for a straight arrangement.The remaining 12 flowers can be aranged only in 1 way as they are all similar.

therefore in a linear arrangement there are 15C3/6 arrangements, => for a circular arrangment the req ans has to be div be 2

Ans = 15C3/12

crack

it is
15!
--------=455 ways
12!*3!

kalyan_iit

14!/12!3!

saurabh_reincarnated

dekho bhai

agar ye itna aasan hota to mein post nahi karta quest. hai na...

the quest. is confusing (it may not be diff) as ans. we get r ridiculous ( i myself got irritating ans- in decimal, huge ones)..

have marked it

bitti_friend ans.

if u calc. it the ans is not in whole no. so it cant be...

and crack the ans cant be that large becos u havent cons. circular perm.

viddyaaa shud we not consider that a group of flowers r alike

so plz. think in another way becos i have spent a lot of time on it

saurabh_reincarnated

well i proceeded this way.

CORRECT ME whr i m wrng

circ. perm so 14! = (15-1)!

garland so divide by half= 14!/2

flowers r alike- divide by may be 11!= (12-1)! and 2! taking circ. permutation

orrr

12! and 3! (which 1 to cons. i m confused)

ans 14!/{2 (12!)(3!)} =/= 19

ans given is 19 but still i doubt if it is correct

rockey

it is 14!/2!(3!)
first arrange 15 flowers.
circ. perm so14!
of these12 are of one type so divide by 12!
3 are of same type so divide by 3!
lastly for garland divide by 2!

saurabh_reincarnated

i said its wrng

rockey

why is it wrong?

saurabh_reincarnated

see prev replies too

its not a whole no thats why...

rv_hbk

My answer is = 91/3.

Method:circular permutations=(n-1)!=14!

But 12 alike of one type & 3 of another.

Hence,ans=14!/12!3!=91/3.

Is that the answer?

saurabh_reincarnated

repeatedly saying countings cant be in decimals, it has to be in whole no...

PLZ. READ PREV.REPLIES BEFORE SENDING IN UR VIEWS

twinkle_star

hey i think the very first reply to this question is correct , u havenot said anything about the arrangement , we just have to arrange it , and it can be possible either in clockwise or anticlockwise directions , so 1/2 (n-1)! is the correct answer

nadeemoidu

The usual formulae for circular permutations and garlands deal only with the cases where all the n are different from each other. so they cannot be used here.

another problem is that u cannot simply divide by 15 saying that its a circular permutation because all the cases may not appear 15 times. to understand this point think of the case where all the 3 flowers of the same type are equidistant from each other. this case appears only once because we 've removed the cases where they repeat 15 times.

One way to do this question is to think in an entirely different way.

The only thing we 've to find out is the no. of ways in which we can place 3 similar flowers in a garland since all the other places will be occupied by the flowers of the other type.

THE ANSWER:
Consider the distances between the 3 flowers of the same type( distance means the no. of flowers between them).

Let them x, y and z
x + y + z = 12 ( only 12 places will be left from the 15 as the other 3 will be occupied by these flowers.)

we ' ve to find the no. of solutions of this equation such x

y

z

u can get this by just finding it manually.
0 0 12
0 1 11
0 2 10
...
0 6 6
..

1 1 10
1 2 9
..
1 5 6

2 2 8
2 3 7
2 4 6
2 5 5

3 3 6
3 4 5
4 4 4

so there are 19 ways.

Ask & Discuss Questions with Community & Experts