Question

11. Number of ways of arranging 4 subjects in 6 periods of a day
a) 1080
b)480
c) 1560
d) 1140​

Answer 1

Answer:

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Answer 2

There are 4 subjects and 6 periods . Each subject be allowed in at least one period .

Three periods will have same subject and remaining four periods will have different subjects .

$Select \: the \: three \: periods \: where \: the \\same \: subject \: is \: taught .$

$This \:can \: be \: done \: in \: ^{6}C_{3}$

$Any \: of \: the \: 4 \: subjects \:can \:be \\organised \: in \: Remaining \: period \: ^{4}C_{1}$

$Remaining \: 2 \: subjects \:can \:be\\arranged \: in \: the \: Remaining \: 4 \: periods \\ in\: 4! \: ways$

$\therefore \red{ Required \: number \: of \: ways}$

$= ^{6}C_{3}\times ^{4}C_{1} \times 4! \\= \frac{6!}{(6-3)! \: 3!} \times \frac{4!}{(4-1)! \: 1!} \times 4! \\= \frac{6!}{3! \times 3!} \times \frac{4!}{(3)! \times 1!} \times 4! \\= 5 \times 4 \times 24 \\= 480$

Therefore.,

$Option \: \pink { ( b ) } \: is \: correct$

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