Permutation-Combination
Aptitude

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Q.

A teacher of $6$ students takes $2$ of his students at a time to a zoo as often as he can, without taking the same pair of children together more than once.

How many times does the teacher go to the zoo?

 A.

10

 B.

12

 C.

15

 D.

20

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Solution:
Option(C) is correct

Two students can be selected from $6$ in ${^6C_2} = 15$ ways.

Therefore, the teacher goes to the zoo $15$ times.


(3) Comment(s)


Pnr
 ()

I guess it should be like ${^6C_2} \times {^4C_2} \times {^2C_2}$ $= 15 \times 6 \times 2$ $=180$ ways

Am I right?



Ram
 ()

If there are 6 students and if he can take 2 at a time and not the same pair each time, then the number of times that he as to go to zoo is just 3!!!!

Am i missing something obvious here???


Isha
 ()

Ram, I guess you are missing the point that it is the not the "same pair"

let's say there are four students

$ABCD$

by your answer, it should be 4 times

BUT

ab
ac
ad
bc
bd
cd

are also pairs hence the teacher would ferry 6 times

Yes, your answer must have been correct only if it would have mentioned that no individual is repeated

I hope you got it :)