A teacher is choosing from her class of 12 students three to represent

Question

A teacher is choosing from her class of 12 students three to represent the school at the local spelling bee. How many different groups of students could the teacher send?

A. 1728
B. 1320
C. 220
D. 132
E. 36

Omkar.kamat · Answer

B. 1320 (12 * 11* 10)

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!

IdiomSavant · Answer

12C3

12! / 3!(12-3)!

12! / 3! * 9!

12 * 11 * 10 / 3!

220

EgmatQuantExpert · Answer

Hey everyone, PFB the solution.

Let us first understand what do we need to apply here – Permutation or Combination ? • The question clearly states that - “ A teacher is choosing” . • This means that the teacher is “selecting” 3 students out of 12 students in her class. Now, whenever we need to do selection without considering arrangement , then we need to apply the concept of “Combination” . Note: • Combination involves only Selection • Permutation involves both Selection AND Arrangement Thus, using combination, in this case, we can write – The total ways of selecting 3 students are =^{12}C_3 = \frac{12!}{3!.9!} = \frac{12 * 11 * 10 *9!}{6 . 9!} = 220 And the Correct Answer is Option C Thanks, Saquib Quant Expert e-GMAT To practise ten 700+ Level Number Properties Questions attempt the The E-GMAT Number Properties Knockout https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

EgmatQuantExpert · Answer

Hey Omkar, It seems that you got confused between arrangement and selection . The solution that you have given is valid if arrangement was required , after selecting the three students. But in this case, we just need to make groups of 3. • So, say if A,B,C are selected, will it matter if I arrange the group as ABC,ACB,BCA,BAC,CBA or CBA? • Doesn't the above 6 cases, refer to the same group consisting of A, B and C? Thus, arranging the groups will not give us any new ways of forming a group . Also, please go through the solution posted by us. It might help you in understanding the mistake that you have made.

Thanks, Saquib Quant Expert e-GMAT To practise ten 700+ Level Number Properties Questions attempt the The E-GMAT Number Properties Knockout https://e-gmat.com/blogs/wp-content/uploads/2016/12/NP-Free-Trial-e1481107541356.png

ScottTargetTestPrep · Answer

We need to determine the number of ways to select 3 students from 12. This is a combination problem, since the order in which the students are selected doesn’t matter. Therefore, the number of ways to select 3 students from 12 is:

12C3 = 12!/3!9! = (12 x 11 x 10)/3! = (12 x 11 x 10)/(3 x 2 x 1) = 2 x 11 x 10 = 220

Answer: C

Abhishek009 · Answer

12C3 = 220 , Answer must be (C)

A teacher is choosing from her class of 12 students three to represent

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A teacher is choosing from her class of 12 students three to represent

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