The number of ways of partitioning the set `{a,b,c,d}` into one or more non empty subsets is

Options

A. `14`
B. `15`
C. `16`
D. `17`

Answer

B

Explanation

`(b)` `{:("Partitioning",,"Number of ways"),(4"members",,1),(1+3"members",,(4!)/(1!3!)=4),(2+2"members",,(4!)/((2!)^(2)2!)=3),(1+1+2"members",,(4!)/((1!)^(2)2!2!)=6),(1+1+1+1"members",,(4!)/((1!)^(4)4!)=1),("Total",,15"ways"):}`