Total number of arrangements:

	p	q	r	s
p	pp	pq	pr	ps
q	qp	qq	qr	qs
r	rp	rq	rr	rs
s	sp	sq	sr	ss

(i)1. With replacement : Sample space (S) = {pp, qq, rr, ss}.
2. Without replacement : Sample space (S') = {pq, pr, ps, qr, qs, rs}
(ii)1. Total = 16; n(S) = 4 ;
\(\therefore p(S) = \frac{4}{16} = \frac{1}{4}\)
2. n(S') = 6;
\(\therefore p(S') = \frac{6}{16} = \frac{3}{8}\).
(b)(i) Numbers divisible by 4: 100, 104, 108, ..., 996.
\(T_{n} = a + (n - 1)d\)
\(996 = 100 + 4(n - 1) \implies 996 = 100 + 4n - 4\)
\(996 = 96 + 4n \implies 4n = 996 - 96 = 900\)
\(n = \frac{900}{4} = 225\)
(ii) Numbers divisible by both 3 and 4 are multiples of 12.
108, 120, 132, ..., 996.
\(996 = 108 + 12(n - 1)\)
\(996 = 108 + 12n - 12 \implies 996 = 96 + 12n\)
\(12n = 996 - 96 = 900\)
\(n = \frac{900}{12} = 75\)