If there are 6 periods on each working day of a school,in how many ways can one arrange 5 subjects such that each subject is allowed at least one period?

1 Answer
yumean1119
Oct 3, 2017

Total 1800 ways.

Explanation:

Under the conditions you mentioned in the question, one subject is assigned two periods and the other four subjects are assigned one period each.

Let the five subjects #A,B,C,D,E# and six periods #1# to #6#.

[Step1] Select the subject assigned two periods and then select two periods which it is assigned.

Number of selection for one subject is #""_5C_1=5# and selection for two periods is #""_6C_2=(6*5)/(2*1)=15#.
The total number of selection in Step1 is #5*15=75#.

[Step2] Assign the other four subjects to four periods.

This step is easy. The total number of selection in Step2 is
#""_4P_4="4!"=24#.

Therefore, there is #75*24=1800# total selections meeting the conditions.

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