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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
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B
1800
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C
360
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D
3600
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Solution

The correct option is B 1800
5 subjects can be arranged in 5C5 ways.
Remaining 1 subject can be selected in 5C1 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 =5C5×5C1×6!2!
=1×5×6!2!
=36002
=1800

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