No. of methods to place 3 boys and 4 girls in a row in such a way that neither two girls G1, G2

M4maths Previous Puzzles

31 Aug 2010 girls and boys

No. of methods to place 3 boys and 4 girls in a row in such a way that neither two girls G1, G2
nor two boys B1, B2 are taken together are

OPtion

1) 2480
2) 1440
3) 1580
4) 1280
5) 2160
6) 2360
7) 2920
8) 2540
9) 2280
10) 2090

Solution

There are three other members besides B1, B2, G1 and G2.
Methods to place these three members = 3.2.1
After then methods to place two boys between them = 4.3
Then methods to place two girls between them = 6.5
Total methods = 3.2.1.4.3.6.5 = 2160

Correct Option: 5 Best Solution (2)

SUDESHNA SEN   13 years AGO

3 boys and 4 girls in a row can be arranged in a row in 7! or 5040 ways.
Now let G1 and G2 be 1 single entity.
Then 7-1 or 6 people can be arranged in 6!*2= 1440 ways.
Similarly, if we take B1 and B2 as 1 single entity then they can also be arranged in ^!*2= 1440 ways.
Again, if we take the two girls G1 and G2 as a single entity and the two boys B1 and B2 as another single entity then the 5 persons can be arranged in 5!= 120 ways.
Therefore, no. of methods to place 3 boys and 4 girls in a row in such a way that neither two girls G1, G2 nor two boys B1, B2 are taken together are= 5040-1440-1440+120= 2280...... Option 9)

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Prabir Sen   13 years AGO

3 boys and 4 girls in a row can be arranged in a row in 7! or 5040 ways.
Now let G1 and G2 be 1 single entity.
Then 7-1 or 6 people can be arranged in 6!*2= 1440 ways.
Similarly, if we take B1 and B2 as 1 single entity then they can also be arranged in ^!*2= 1440 ways.
Therefore, no. of methods to place 3 boys and 4 girls in a row in such a way that neither two girls G1, G2 nor two boys B1, B2 are taken together are= 5040-1440-1440= 2160...... Option 5)

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