In how many ways can five people be divided into three groups? (b) In how many ways can five people be distributed in three different rooms if no room must be empty? In how many ways can five people be arranged in three different rooms if no room must be empty and each room has 5 seats in a single row.

Explanation

5->1,1,3

`(5!)/(3!*1!*1!*2!)=10`

5->1,2,2

`(5!)/(11*2!*2!*2!)=15`

Total groups=25

c)5->1,1,3 =10

3 different rooms

`5C_1*5C_1*5C_3*3!-(1)`

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