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?

For Competitive Exams

10th CBSE Maths

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

1200

1800

1900

Explanation:

5 subjects can be arranged in 6 periods in $^6P_{5}$ ways.

Any of the 5 subjects can be organized in the remaining period ( $^5C_{1}$ ways).

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

Total number of arrangements

$\dfrac{^6P_{5}\times^5C_{1}}{\left(2!\right)}$

=1800

Next Question

In a chess competition involving some men and women, every player needs to play exactly one game with every other player. It was found that in 45 games, both the players were women and in 190 games, both players were men. What is the number of games in which one person was a man and other person was a woman?

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