Question

A class has 21 students. The class teacher has been asked to make n groups of r students each and go to the zoo taking one group at a time. The size of the group i.e. the value of r for which the teacher goes to the zoo, the maximum number of times is (no group can go to the zoo twice).
A. 9 or 10
B. 10 or 11
C. 11 or 12
D. 12 or 13

Answer 1

Hint:
In probability, \[{}^n{C_r}\] is the number of ways of selection of \[r\] elements from a set of \[n\] elements, such that the order of elements does not matter.

Formula Used:
 \[{}^n{C_r} = \frac{{n!}}{{r!(n - r)!}}\]


Complete step-by-step answer:
Compute the maximum number of times:
Given, that there are 21 students.
Since the teacher must make n groups of r students, so the number of groups formed =\[{}^{21}{C_r}\]
The number of times the teacher goes to the zoo is the highest when the number of groups formed is the highest.
The size of the group i.e., the value of r for which the teacher goes to the zoo, the peak number of times is (no team can go to the zoo two times).
\[r = \frac{{21 - 1}}{2}or\frac{{21 + 1}}{2}\]
\[r = \frac{{20}}{2}or\frac{{22}}{2}\]
\[r= 10\] or \[11\]
Therefore the correct answer is Option B.


Note: The combination is how objects from a set can be chosen, usually without replacement, to form subsets. This selection of subsets is known as a combination when order is not a factor. A combination of r items from a total of n items is signified as \[{}^n{C_r}\]