Question

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

• A. $210$
• B. $1800$
• C. $360$
• D. $3600$

Answer 1

The correct option is B $1800$

5 subjects can be arranged in ${}^5{C}_5$ ways.

Remaining 1 subject can be selected in ${}^5{C}_1$ ways.

These 6 subjects can be arranged themselves in $6!$ ways

Since two subjects are same, we need to divide by $2!$

Total number of arrangements $=\frac{{}^5{C}_5{\times }^5{C}_1\times 6!}{2!}$

$=\frac{1\times 5\times 6!}{2!}$

$=\frac{3600}{2}$

$=1800$