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?
To find: number of ways of arranging 5 subjects in 6 periods.
Condition: at least 1 period for each subject.
5 subjects in 6 periods can be arranged in P (6,5).
Remaining 1 period can be arranged in P (5,1)
Formula:
Number of permutations of n distinct objects among r different places, where repetition is not allowed, is
P(n,r) = n!/(n-r)!
Total arrangements = P(6,5) × P(5,1) = 
× 
= 
× 
= 720 × 5 = 3600.
Total number of ways is 3600 ways.
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