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  4. There are six periods in each working day of a school. Number of ways in which 5 subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

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Q. There are six periods in each working day of a school. Number of ways in which $5$ subjects can be arranged if each subject is allotted at least one period and no period remains vacant is

Permutations and Combinations

Solution:

Atleast one period is repeated, which can be selected in ${ }^{5} C_{1}$ ways.
Now $6$ subjects can be arranged in $\frac{6 !}{2 !}$ ways.
Hence total number of ways are $5 \times \frac{6 !}{2 !}=1800$