JAMB Mathematics Past Questions & Answers - Page 324

2q3₅ = 77₈

2 x 5² + q x 5¹ + 3 x 5⁰ = 7 x 8¹ + 7 x 8⁰

2 x 25 + q x 5 + 3 x 1 = 7 x 8 + 7 x 1

50 + 5q + 3 = 56 + 7

5q = 63 - 53

q = \(\frac{10}{5}\)

q = 2

Man lives = \(\frac{2}{3}\) not live = \(\frac{1}{3}\)

Wife lives = \(\frac{3}{5}\) not live = \(\frac{2}{5}\)

P(at least one lives to 80 years) = P(man lives to 80 not woman) + P(woman lives to 80 and not man) + P(both live to 80)

\(P = (\frac{2}{3} \times \frac{2}{5}) + (\frac{2}{5} \times \frac{1}{3}) + (\frac{2}{3} \times \frac{3}{5})\)

= \(\frac{4}{15} + \frac{3}{15} + \frac{6}{15}\)

= \(\frac{13}{15}\)

Pass(P) = \(\frac{2}{3}\), Fail(F) = \(\frac{1}{3}\)

T = P.P.F ==> \(\frac{2}{3} \times \frac{2}{3} \times \frac{1}{3}\) = \(\frac{4}{27}\)

\(\frac{8!}{3!}\)

\(\frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{3 \times 2\times 1}\)

==> 8 x 7 x 6 x 5 x 4 = 6720

\(\frac{n + 1 (n - 2)}{(n + 1)!}\)

\(\frac{(n + 1) + (n - 2)!(n - 2)!}{(n + 1)!}\)

\(\frac{(n + 1)(n + 1 -1)(n+1-2)(n+1-3)!}{3!(n-2)!}\)

\(\frac{(n + 1)(n)(n-1)(n-2)!}{3!(n-2)!}\)

\(\frac{(n + 1)(n)(n-1)}{3!}\)

Since n = 15

\(\frac{(15 + 1)(15)(15-1)}{3!}\)

\(\frac{16 \times 15 \times 14}{3 \times 2 \times 1}\)

= 560