(A) We have $6$ periods and $5$ subjects. Since each subject must be taught at least once,one subject must be repeated twice,and the other $4$ subject

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(A) We have $6$ periods and $5$ subjects. Since each subject must be taught at least once,one subject must be repeated twice,and the other $4$ subjects must be taught once each.First,we choose the subject to be repeated in $^5C_1 = 5$ ways.Now,we have $6$ subjects (including the repetition) to be arranged in $6$ periods.The number of arrangements is given by the permutation of $6$ items where $2$ are identical:$\frac{6!}{2!} = \frac{720}{2} = 360$.Therefore,the total number of ways is $5 \times 360 = 1800$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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There are $6$ periods in each working day of a school. The number of ways one can arrange $5$ subjects such that each is allowed at least one period is:

MHT CET 2022 All MHT CET

A
$1800$
B
$725$
C
$720$
D
$5$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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