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  • 7 periods make up every school working day. 6 subjects can be arranged in how many different ways as long as each receives at least one period.Option: 1

7 periods make up every school working day. 6 subjects can be arranged in how many different ways as long as each receives at least one period.

Option: 1

13120


Option: 2

15120


Option: 3

16310

 


Option: 4

18210


Answers (1)

best_answer

The 6 subjects can be arranged in 7 periods given by,

^{7}P_6

The remaining 1 period can be arranged in  ^{6}P_1  ways.

Two subjects are alike in each of the arrangements. 

So we need to divide by 2! to avoid overcounting. 

Thus, the total number of arrangements is given by,

\begin{aligned} & \frac{\left({ }^7 P_6 \times{ }^6 P_1\right)}{2 !}=\frac{5040 \times 6}{2} \\ & \frac{\left({ }^6 P_5 \times{ }^5 P_1\right)}{2 !}=\frac{3600}{2} \\ & \frac{\left({ }^7 P_6 \times{ }^6 P_1\right)}{2 !}=15120 \end{aligned}

Therefore, the total number of ways is 15120 ways.

Posted by

Ritika Jonwal

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