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Maths Puzzle
Numerical Ability
Permutation and Combination
How many methods are possible for arranging 5 boys and 4 girls in such a way that no 2 girls could sit together?
Read Solution (Total 13)
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- Solution given by site administrator for same puzzle ( earlier) was not correct.
The arrangement can be done as below
X..B..X..B...X..B...X..B...X..B..X
where b is the position of Boys and 4 girls can be placed at any of 6 positions marked as X.
so Number of arrangements will be
5! * 6p4 = 120*360 = 43200 - 13 years agoHelpfull: Yes(12) No(2)
- Number of methods will be
5! * 6p4
as 4 girls can be placed at the locations marked by X in
XBXBXBXBXBX
120*6*5*4*3=120*360 - 13 years agoHelpfull: Yes(5) No(0)
- 5!*6!/(6-4)!=5!*6!/2=120*720/2=43200
- 13 years agoHelpfull: Yes(4) No(2)
- 5 boys In 5 places so 5 chances
in between boys and around them total 6 places in that 6 places yo6p4
u need to select 4 girls and arrange them in 4 places for that we need permutation so 6p4
so ans is 5*6p4
x b x b x b x b x b x - 8 years agoHelpfull: Yes(3) No(0)
- _B_B_B_B_B_
no of ways for arranging 5 boys =5!
no of ways for arranging 4 girls=7c4*4!
so total ways of arranging 5 boys and 4 girls under above condition=5!*7c4*4!=100800 - 13 years agoHelpfull: Yes(2) No(6)
- boys can be arrranged in 5! and girls in 6P4 so final sol is 5!*6P4
- 8 years agoHelpfull: Yes(1) No(0)
- Answer: 359280
Total no of method for arranging the 9 people(5B+4G)=9P9.
Divide the four girls in two group where each group having two girls.
Now....we have the situation like the following.....
___B___B___B___B__B___
means we have 6 blank space in which we have to select 2 for two groups.and further more these group member can be arrange 2P2 ways.
So total number for arranging 9 people in which two girls sitting together is 5P5*(6C2*2P2)
Now total number of method for arranging the 5B and 4G such that NO 2 girls could sit together are:
9P9 - 5P5*(6C2*2P2)=359280 - 9 years agoHelpfull: Yes(0) No(2)
- girls in 4! ways and boys 3! ways
therefore 4*4!*5!=576 - 8 years agoHelpfull: Yes(0) No(2)
- 5!*4!/2!=360
- 8 years agoHelpfull: Yes(0) No(2)
- there are 5 boys and place where girls can sit 6 so,
5!*6p4= 43200 - 7 years agoHelpfull: Yes(0) No(0)
- 5!*6!/(6-4)!=5!*6!/2=120*720/2=43200
- 7 years agoHelpfull: Yes(0) No(0)
- 4 may be correct
- 5 years agoHelpfull: Yes(0) No(0)
- first we will placed the person in order to boy ,girl,boy,girl,boy,girl,boy,girl,boy
- 1 Month agoHelpfull: Yes(0) No(0)
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