A class consists of 12 girls and 10 boys. In how many ways can the

Question

A class consists of 12 girls and 10 boys. In how many ways can the class form a line if the girls always remain in order from shortest to tallest within the line and the boys always remain in order from tallest to shortest within the line?

A.  12!

B.  12!*10!

C.  \frac{22!}{10!}

D.  \frac{22!}{12!}

E.  \frac{22!}{10!*12!}

PyjamaScientist · Accepted Answer

There are  12   girls and  10   boys in the class.  (lucky boys, never had that ratio in my life) #sciencestudent

So, we need to find the number of cases when all the girls and boys are standing in the ascending order of heights. There is a total of 22 students. So, if I do  22!  that would give me  ALL   the possible arrangements of these 22 students. Isn't it? However, to compensate for the fact that the boys and girls have to be arranged as per their heights, we need to divide by the number of ways the boys can be ordered, because there is actually only  1 valid way  to order the boys for each of the  10!  and only  1 valid way  to order the girls for each of the  12! .
Thus, the answer would be (E) :  \frac{22!}{(12!*10!)}

Vartika2525 · Answer

Can someone explain why B is wrong?

Madhvendrasinh · Answer

option B is wrong because there is no such codition as that the girls must be together or the boys must be together.

According to option B we add girls in the line the from shortest to tallest and then we add boys to the line from tallest to shortest,
G G G G G G G G G G G G (12!) B B B B B B B B B B (10!)

but since it is possible that the line would contain boys and girls in mix but in their respective correct order
    G   B  G G B G B B B G G G G G B B G B G B  G   B   
 Here,  
Blue= Tallest in their respective group
Red= Shortest in their respective group.

Hence there possible combinations will be out of 22 since there is a total of 22 places and they are interchangeable for any position so,  
  22!/12!*10!  option E

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

A class consists of 12 girls and 10 boys. In how many ways can the

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A class consists of 12 girls and 10 boys. In how many ways can the

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards