Discussion Problem_ (4)

[duck]

In a class of 10 students there are 3 girls A,B and C. In how many
ways can they be arranged in a row such that no two girls
are consecutive?

[VR]

there will be 8C3.3!7!

[Mauli]

7! ways n which the boys can be arranged.
A,B,C can then be arranged in 8P3 ways
so 7!*8P3

[Sumit]

Total no. of ways 10 students can be arrange= 10!
total no. of ways in which all the 3 girls sit together =8!*7!
total no. of ways in which exactly 2 girls sits together =there will be two scenario: a)two girls sits together but not on extreme two seats.(i.e starting 2 seats or ending two seats from seats 1 to 10)
b) two girls sits on extreme seats(i.e either starting 2 or ending 2)

So, a)=3C2*2!*6C1*7!.
b)=2(3C2*2!*7C1*7!)

So, the answer is=10!-(8!*7!)-(3C2*2!*6C1*7!)-2(3C2*2!*7C1*7!).

plz confirm whether this sol is correct or not...

[duck]

There are 7! ways in which boys can be arranged. Now, we have 8 places in which we can arrange 3 girls (since we want no two girls to sit together).So, girls can be arranged in 8*7*6 ways or [(8!/5!) ways] .
Therefore, total number of ways = 7!*8*7*6

_B_B_B_B_B_B_B_