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.