There are 5 eligible Gujarati grooms of which 2 know Bengali and 5 eligible Bengali grooms of which

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09 Aug 2016 Bride And Groom

There are 5 eligible Gujarati grooms of which 2 know Bengali and 5 eligible Bengali grooms of which 3 know Gujarati. There are 5 eligible Gujarati and 5 eligible Bengali brides. An eligible bride is agreeable to marry a boy of his community or a boy who knows her language. Grooms have no choice. In how many different ways 10 couples can be formed.

OPtion

1) 16550
2) 14400
3) 12000
4) 120
5) 256920
6) 435680
7) 37200
8) 16340
9) 144000
10)12800

Solution

In 5 eligible Gujarati grooms, 2 know Bengali, remaining 3 should make their pair with Gujarati girls.
No. of methods to make such couple = 5.4.3 = 60
Similarly in 5 eligible Bengali grooms, 3 know Gujarati, remaining 2 should make their pair with Bengali girls.
No. of methods to make such couple = 5.4 = 20
No. of methods to make remaining 5 couple = 5.4.3.2.1 = 120
Hence total no. of methods = 60*20*120 = 144000

Option 9)

Correct Option: 9 Best Solution (11)

G.S.Kantharao   8 years AGO

There are 3 chances
1. 5 brides marry 5grooms
Then the total ways are5!*5!*=120*120=14400
2. 5 Bengali brides can marry 4 Bengalii grooms and 1 Gujarathi groom. Then the number of ways is= 3c1*2c1*5!*5! = 6*14400
3. 5Bengali brides can marry 3Bengali grooms and 2 Gujarathi grooms.
Then the ways are 3c2*2c2*5!*5!= 3*14400
Then the total number of ways= 14400+6*14400+3*14400
=10*14400=144000
Hence the right choice is 9

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SANDEEP KUMAR MAHATO   8 years AGO

There are only 3 cases possible

CASE-1) 5 punjabi brides marry to 5 punjabi grooms and
5 bengali brides marry to 5 bengali grooms

so total cases = 5!*5! = 14400

CASE-2) 5 punjabi brides marry to 4 punjabi & 1 bengali groom

so total cases = 3C1*2C1*5!*5! = 86400

CASE-3) 5 punjabi brides marry to 3 punjabi & 2 bengali grooms

so total cases = 3C2*2C2*5!*5! = 43200

now adding all these 3 cases for formation of 10 couples

14400 + 86400 + 43200 = 144000

option 9)

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KUMARA S K   8 years AGO

5 grooms - 2 knows bengali = 5!/2! = 60
5 grooms bengali - 3 knows gujarati = 5!/3! = 20
all couples = 5! = 120
couples formed = 60*20*120 = 144000

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Shiv Pandey   8 years AGO

3 gujrati groom can make couple only with gujrati brides
So, ways=5*4*3=60
2 bengali groom can make couple only with bengali brides
So, ways=5*4=20
remaining 5 (i.e 2 gujrati and 3 bengali) will make couple in 5*4*3*2*1 ways= 120 ways
So, different ways = 60*20*120 = 144000 ways

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prashant kumar   8 years AGO

first of all we hav 5 groom who are eligible for all the brides so we are left with 3 gujrati who can mary only gujrati bride and 2 bengali who can mary only bengali bride so selection and arrangement fr then will be (5p3)*(5p2) and then other 5 couple arranged among themselves so factorial of 5 so final equation will be (5p3)*(5p2)*fact5=144000

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himabindu   8 years AGO

there are three possible ways

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yerra anitha   8 years AGO

in 5 eligible gujarathi grooms 2know bengali,remaining 3 should make thie r pair with gujarathi girls.
no of methods to make such couple in 5.4.3 ways ie..60 and in same way for Bengali grooms can be arranged in 5p2 ways remaining can be done in 5p5 ways finally 10 couple scan be arranged in =5p3.5p2.5p5=144000

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Rips Andy   8 years AGO

In the Gujrati Grooms knows bengali= 2
Therefore, Gujrati pair= 5*4*3=60
Similarly, in Bengali Grooms knows gujrati = 3
Therefore, Bengali pair= 5*4= 20
No of couples formed= 120
total 10 couples are= 120*20*60= 144000

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sandeep kumar   8 years AGO

In 5 eligible Gujarati grooms, 2 know Bengali, remaining 3 should make their pair with Gujarati girls.
No. of methods to make such couple = 5.4.3 = 60
Similarly in 5 eligible Bengali grooms, 3 know Gujarati, remaining 2 should make their pair with Bengali girls.
No. of methods to make such couple = 5.4 = 20
No. of methods to make remaining 5 couple = 5.4.3.2.1 = 120
Hence total no. of methods = 60*20*120 = 144000

Like? Yes | No   

Mukund Manohar   8 years AGO

In 5 eligible Gujarati grooms,2 know bengali,remaining 3 should make their pair with Gujarati girls
No. of methods to make such couple = 5*4*3 = 60
Similarly in 5 eligible Bengali grooms,3 know gujarati,remaining 2 should make their pair with Bengali girls
No. of methods to make such couple = 5*4 = 20
No. of methods to make remaining 5 couple
= 5*4*3*2*1
=120
Total number of methods = 60*20*120 = 144000

Like? Yes | No (1)  

Vaishali   8 years AGO

By using permutations and combinations
(5c5*5c5)+(5c......

Like? Yes | No (3)