bhumika.k.shah wrote:Hey ,
Could you elaborate further on how u got the highlighted part ?
harsh.champ wrote:rahul.s wrote:5 actresses A, B, C, D and E are vying for the 3 leading roles in a new film. assuming that no actress has any advantage in getting any role, what is the probability that A and B will star in the film together?
[spoiler]OA is 3/10 [/spoiler]
[spoiler]my solution: 1/5 * 1/4 = 1/20. where did i make a mistake?[/spoiler]
Hey rahul.s,
Did u delete ur post after posting for the 1st time??
As for the soln.,
A and B will star together.Now, the remaining 1 role can be selected in 3C1 ways.
Also,3!ways in which roles can be interchanged.
Total no. of ways = 5P3 = 60
Hence, 3x6/60 = 3/10 which is the OA.
I hope you can now see your mistake.
You dont have to consider separately as you did over here.
my solution: 1/5 * 1/4 = 1/20.
The italics text was given by rahul.s.
The bold-faced text by me.
Which part did you not understand??
Anyways I will explain how I did it.
3 roles(suppose R1 ,R2 and R3 ) are there.
If A and B star together , only 1 role is left .The 3rd actress can be selected among the remaining 3 left in 3C1 ways.
Now, they can
also interchange the roles between them in 3! = 6 ways.
So,no. of ways = 6 x 3 =18 .
For total no. of ways ,we can select the 3 roles among 5 actresses in
5C3(5!/3! x 2!) ways.
Also they can interchange the roles betweeen them in 3! ways.
So,
total no.. of ways = 5C3 x 3! = 60 ways . [5C3 x 3! = 5P3 = 5! / 2!]
So, the ans. is 18/60 = 3/10.
I hope my soln. approach is clear to you Bhumika or I can elaborate more if you want.It takes time and effort to explain, so if my comment helped you please press Thanks button
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