Question

A class has $21$ students. The class teacher has been asked to make $n$ groups of $r$ students each and go to zoo taking one group at a time. The size of group for which teacher goes to the maximum number of times is:

• A. $9$
• B. $10$
• C. $11$
• D. $12$

Answer 1

Answer: (B), (C)

The total number of students in class is 21.

Now,

Number of group of r students in each group can be formed in ${}^{21}{C}_r$ ways.

Number of times the teacher can go to the zoo = Number of groups (G) she can form = ${}^{21}{C}_r$

Z is maximum when G is maximum

i.e. for n to be maximum

$r=\frac{21-1}{2}or\frac{21+1}{2}$

$\Rightarrow r=10or11$

The teacher goes the maximum number of times is 10 or 11

Hence, option (B) and (D) are correct.