[1800] There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects su

For Competitive Exams

There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

3200

None of these

1800

3600

Explanation:

5 subjects can be arranged in 6 periods in ⁶P₅ ways.

Any of the 5 subjects can be organized in the remaining period ⁵C₁ ways.

Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.

Total number of arrangements

$=\dfrac{~^{6}P_5 × ~^5C_1}{2!}=1800$

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