Refresher - MATHEMATICS Quiz 22
PROBLEM 1:
Suppose a poker hand is dealt to an engineer at a casino and the
engineer would like to know how many poker hands are possible when 5
cards are dealt from 52.
Solution:
n!
No. of ways =
(n - r)! r!
52!
No. of poker hands =
(52 - 5)! 5!
No. of poker hands = 2,598,960
, Refresher - MATHEMATICS Quiz 22
PROBLEM 2:
Many bridges are built of steel-reinforced concrete. As long as the steel is
protected from corrosion, the bridge lives are very long. The cast difference
between proper maintenance and early replacement is also very large. For
example, a particular bridge would cost $200,000 now to repair or $1.8M in 10
years to replace. The state highway department claims it uses an interest rate of
8%, but it has decided to replace the bridge later due to a current shortage of
funds. The state agency also anticipates some federal funding for the
replacement bridge. What is the implied interest rate for choosing to replace later
rather than to repair now?
Solution:
0 1 2 3 4 5 6 7 8 9 10
1800000
200000
A = P(1 + i)n
1,800,000 = 200,000(1 + i)10
(1 + i)10 = 9
(1 + i) = (9)1/10
1 + i = 1.246
i = 24.6%
PROBLEM 1:
Suppose a poker hand is dealt to an engineer at a casino and the
engineer would like to know how many poker hands are possible when 5
cards are dealt from 52.
Solution:
n!
No. of ways =
(n - r)! r!
52!
No. of poker hands =
(52 - 5)! 5!
No. of poker hands = 2,598,960
, Refresher - MATHEMATICS Quiz 22
PROBLEM 2:
Many bridges are built of steel-reinforced concrete. As long as the steel is
protected from corrosion, the bridge lives are very long. The cast difference
between proper maintenance and early replacement is also very large. For
example, a particular bridge would cost $200,000 now to repair or $1.8M in 10
years to replace. The state highway department claims it uses an interest rate of
8%, but it has decided to replace the bridge later due to a current shortage of
funds. The state agency also anticipates some federal funding for the
replacement bridge. What is the implied interest rate for choosing to replace later
rather than to repair now?
Solution:
0 1 2 3 4 5 6 7 8 9 10
1800000
200000
A = P(1 + i)n
1,800,000 = 200,000(1 + i)10
(1 + i)10 = 9
(1 + i) = (9)1/10
1 + i = 1.246
i = 24.6%
