There are 20 questions in a question paper. If no two students solve the same combination of questions but solve equal number of questions then the maximum number of students who appeared in the examination is
A.
$$^{20}{C_9}$$
B.
$$^{20}{C_{11}}$$
C.
$$^{20}{C_{10}}$$
D.
None of these
Answer :
$$^{20}{C_{10}}$$
Solution :
If $$r$$ questions are solved by each student then the number of possible selections of questions is $$^{20}{C_r}.$$
∴ the number of students $$= {^{20}{C_r}}.$$
($$\because $$ each student has solved different combinations of questions)
∴ the maximum number of students = maximum value of $$^{20}{C_r} = {\,^{20}}\,{C_{10}},$$ because $$^{20}\,{C_{10}}$$ is the largest among $$^{20}{C_0},{\,^{20}}{C_1},.....{,^{20}}{C_{20}} - $$ being the middle one.
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is