Question

How many words can be formed using letter of UNIVERSITY using
each letter at most once?
i) If each letter must be used,
ii) If some or all the letters may be omitted.

Answer 1

1) The word UNIVERSITY contains 9 letters, each letter contain,
U=1,
N=1,
I=2,
V=1,
E=1,
R=1,
S=1,
T=1,
Y=1.
9!/2!=1*2*3*4*5*6*7*8*9/1*2
=3*4*5*6*7*8*9
=181440 arrangement is possible.
(2). 9!=1*2*3*4*5*6*7*8*9
=362880//.