Seven different lecturers are to deliver lectures in seven periods of a class on a particular day. $$A, B$$ and $$C$$ are three of the lecturers. The number of
ways in which a routine for the day can be made such that $$A$$ delivers his lecture before $$B,$$ and $$B$$ before $$C,$$ is
A.
420
B.
120
C.
210
D.
None of these
Answer :
None of these
Solution :
As the order of $$A, B, C$$ is not to change they are to be treated identical in arrangement. So, the required number of ways $$ = \frac{{7!}}{{3!}}.$$
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