Answer
a) 60
b)10
Work Step by Step
S={1, 2, 3, 4, 5}.
a) Number of 3-permutations of S will be $^5C_3$, since we have to choose 3 from 5 elements and these permutations can be arranged in 3! ways.
So, number of 3-permutations are $^5C_3$. 3!=60 and which are
123$\quad$132$\quad$213$\quad$213$\quad$312$\quad$321
124$\quad$142$\quad$412$\quad$421$\quad$214$\quad$241
125$\quad$152$\quad$251$\quad$215$\quad$512$\quad$521
134$\quad$143$\quad$341$\quad$314$\quad$413$\quad$431
135$\quad$153$\quad$531$\quad$513$\quad$315$\quad$351
145$\quad$154$\quad$541$\quad$514$\quad$415$\quad$451
234$\quad$243$\quad$324$\quad$342$\quad$423$\quad$432
235$\quad$253$\quad$523$\quad$532$\quad$325$\quad$352
345$\quad$354$\quad$453$\quad$435$\quad$534$\quad$543
245$\quad$254$\quad$524$\quad$542$\quad$425$\quad$452
b) Number of 3 combinations are $^5C_3$=10
123,124,125,134,135,145,234,235,345,245.
