How many ways are possible to arrange 4 boys and 3 girls for a dinner, if there are two straight b

M4maths Previous Puzzles

19 May 2010 Arrange boy and girl

How many ways are possible to arrange 4 boys and 3 girls for a dinner, if there are two straight benches
of capacity 5 and 2 persons for their sitting?

OPtion

1) 720
2) 5040
3) 2520
4) 840
5) 4320
6) 2460
7) 2860
8) 120
9) 24
10) 1

Solution

Total no. of persons = 7
Since benches are straight, therefore arranging them in benches of capacity 5 and 2 persons is
equivalent to arranging them in a straight bench of capacity 7 persons.
Total no. of methods = 7*6*5*4*3*2*1 = 5040

Correct Option: 2 Best Solution (9)

Prashant Khare   15 years AGO

There are two ways to think
1) Since there are straight benches and no other condition imposed its just a permutation of 7 people so ans is 7! = 5040.
2)Take 5 persons first in 7C5 ways then arrange them in 5! ways and then arrange the rest two in 2! ways which gives 7C5*5!*2! = 5040
But i missed in 1 min :(

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~Sandeep~   15 years AGO

7C2 * 5! * 2!

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Rohit Agrawal   15 years AGO

7c5 * 120 *2

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Karthik Pandiyan   15 years AGO

7!=5040

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ASHOK ROY   15 years AGO

5 persons from 7 persons can be arranged ib 2520 ways and remaining 2 can be arranged in 2 ways . Total number of ways those persons can be arranged is 5040 ways

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Aman   15 years AGO

7!=5040

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SUDESHNA SEN   15 years AGO

4+3= 7 persons can be arranged in 5+2 seats in 7P7= 7*6*5*4*3*2*1= 5040 ways..... Option 2)

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Mamon Sengupta   15 years AGO

4+3= 7 persons can be arranged in 5+2 seats in 7P7= 7*6*5*4*3*2*1= 5040 ways..... Option 2)

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Trishita Dasgupta   15 years AGO

4+3= 7 persons can be arranged in 5+2 seats in 7P7= 7*6*5*4*3*2*1= 5040 ways..... Option 2)

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