There are 3 boys and 4 girls. We have to arrange any 1 boy at the centre and any 2 girls at corners.

M4maths Previous Puzzles

21 Oct 2011 boys and girls

There are 3 boys and 4 girls. We have to arrange any 1 boy at the centre and any 2 girls at corners. In how many methods these persons can be arranged.

OPtion

1) 432
2) 488
3) 512
4) 580
5) 624
6) 725
7) 864
8) 1024
9) 1200
10) none of these

Solution

methods for arranging 1 boy at centre = 3
methods of arranging 2 girls at corner = 4*3 = 12
methods of arranging remaining 4 persons = 4*3*2*1 = 24
so total methods = 3*12*24 = 864

Correct Option: 7 Best Solution (12)

Dr.Dipin Singh   12 years AGO

4 persons can be placed in 4 unconditional places in 4*3*2= 24 ways
4 girls can be placed in 6 ways at two corner and by replacing corners among two girls, there are 12 ways.
3 boys can be placed in centre in 3 ways.

so total methods = 24*12*3 = 864

Like? Yes (7) | No   

Jeevan   12 years AGO

3*(2*6)*(4*3*2) = 864 methods ... option 7

Like? Yes (5) | No   

Kunal Anand   12 years AGO

to selct 1 boy out of 3 = 3c1= 3
to selct 2 girl out of 4 and then rearrange itself = 4c2*2! = 12
now 2 boys and 2 girls remaining these will arrange in 4! = 24 ways
so, overall possible no. of arrangement = 3*12*24 = 864

Like? Yes (5) | No (1)  

Maheshkumar Eaga   12 years AGO

two girls at corner their selection will be: 4p2= 4*3=12------------(a)
one boy at centre his selection 3p1=3----------------(b)
remaining 2 girls and 2 boys thier selection from total 4 members i,e remaining boys and girls
reamaining total boys and girls are 4
therefore
remaining selection will be= 4p4=4*3*2=24-------(c)
total selection is= a*b*c=12*3*24=864

Like? Yes (3) | No (1)  

krishna kumar gupta   12 years AGO

1 2 3 4 5 6 7
g 2 3 b 5 6 g

now 2 girls and 2 boys can be arranged by following ways at 4 places=3c1*4c2*4!=3*6*24=432;
and girls at 1st and 7th position can also be arranged by 2! ways.
so total ways=2*432=864.

Like? Yes (3) | No (2)  

sonal poddar   12 years AGO

The boy at the centre can be chosen in 3 ways.similarly the corner girls can be chosen as 4x3 ways.remaining 4 persons can be arranged in 4! ways.
so,total number of ways in which they can be arranged=3x4x3x4!=864 ways.

Like? Yes (1) | No   

SIKENDER KHAN   12 years AGO

for fix places::: 4*3 for girls and 3 for boys that means
4*3*3,then for remaining places factorial 4.
that will give.4*3*2.
hence total methods will be.
4*3*3*4*3*2*1=864

Like? Yes (2) | No (1)  

RAKESH BALAN   12 years AGO

total 7 places.......for 4 places the possibilities are(3g 4b 3b 2b)or(4b 3g 3b 2b)or (4b 3b 3g 2b) or(4b 3b 2b 3g)......therefore (3*4*3*2)*4=288...
next for 3 places (1g 1b 1b)or (1b 1g 1b) or(1b 1b 1g)....so (1*1*1)*3=3...........finallly 288*3=864

Like? Yes (2) | No (1)  

Karan Kosta   12 years AGO

bcos at first place & last place only girl can sit so 4*3 now 1 boys at centerthen total ways is 4*3*3.
4 vacancies are available methodes is 4!.
now total ways for arrangement is 4*3*3*4!=864

Like? Yes (2) | No (1)  

Subhankar Mondal   12 years AGO

for center 3c1.For corner(4c2*2!).Rest place 4!
so, ans is 3c1*(4c2*2!)*4!=864

Like? Yes (2) | No (1)  

phani   12 years AGO

(2*4C2)*(3C1)*(4C4*4!)
two girls at ends can be arranged in (2*4C2)
middle boy in (3C1)
remaining in (4C4*4!)

Like? Yes (1) | No   

sridhar reddy   12 years AGO

3 boys and 4 girls
no.of ways a boy sits in the middle is 3
no of ways 2 girls sits on both sides is 4*3=12
the no.of ways remaining 4 places should be filled
with 2 boys and 2 girls is 4*3*2*1=24
the total no.of ways to arrange is 3*12*24=864

Like? Yes (2) | No (1)