Six periods are to be allotted to five subjects such that each subject has atleast one period. The n

Question

Six periods are to be allotted to five subjects such that each subject has atleast one period. The number of ways in which this can be done is

Professor PC Thomas Classes · Answer

One of the subjects should be given two periods. Choose it. This can be done is ${ }^5 \mathrm{C}_1$ ways .The six subjects (one repeated) can be arranged in $\frac{6!}{2!}$ ways. Total possibilities is $\frac{5}{2}(6!)$