MATH 55(31) WD SMITH HOMEWORK #6 answers
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1. Carbon-14 has half-life 5730 years.
What fraction carbon14 left after 9000 years?

            (9000/5730)
ANS:   (1/2)               =  0.3366495338


2. How many possible license plates of form AXQ-730
(3 letters then 3 numbers)?

           3   3
ANS:     26  10  =  17576 * 1000 =  17576000


3. For 100 people you pick a 5-person team. How many possible teams
(where {joe, mary, ellen, tom, anne} counts as SAME team as
{ellen, anne, joe, tom, mary})?

*WRONG ANS:   100*99*98*97*96

would be the number of teams (100 ways to pick first team member,
99 to pick second, 98 to pick third, etc.) EXCEPT this would count
different orders of the same team as "different" teams.  There are
120 = 5! = 5*4*3*2*1  possible orderings of the team so this
would overcount by a factor of 120.
So to correct we have to divide by 120.
                                    100!              100
RIGHT ANS:   100*99*98*97*96/120 = ------ =    C   = (   ) = 75287520.
                                   5! 95!   100 5      5

to give several different possible - all equivalent - expressions.


4. Secret 3-letter password like AXQ, but not allowed to repeat a letter
(AAZ, BQB illegal). How many passwords?

Ans:   26*25*24 =   15600 =    P
                             26 3 .

5. Toss a red die and a blue die.
Probability they add up to 10 is?


ANS:  See the book 7A...  there are 36 possible outcomes 
    red+blue = 1+1, 1+2, 1+3,..., 6+4, 6+5, 6+6
(6 possibilities for red, 6 for blue, so 6*6=36 combinational possibilities)
and among these, exactly these 3:  red+blue = 4+6, 5+5, 6+4     add up to 10.
So probability is 3/36 = 1/12 =  .08333333333.
Also: see table 7.3 in section 7A of book where this is worked out for you...