If the exclusion of Miss Jones and Mr Smith serving together was not present, the are 15C4 = 1365 ways of selecting the committee.
Miss Jones can serve on the committee in the following ways:
a) with 3 men
b) with 2 men and another woman
c) with 1 man and 2 other women
d) with 3 other women.
Arrangement d) obviously presents no restrictions.
Arrangement a) has 7C3 ways excluding Mr Smith, and 8C3 ways if Mr Smith was included.
Arrangement b) has 7C2 * 6 ways excluding Mr Smith, and 8C2 * 6 ways if Mr Smith was included.
Arrangement c) has 7 * 6C2 ways excluding Mr Smith, and 8 * 6C2 ways if Mr smith was included.
The reductions in ways caused by the restriction are as follows:
a) 8C3 - 7C3 = 21 ways
b) 6(8C2 - 7C2) = 42 ways
c) 6C2 = 15 ways
The total reduction in the number of ways is: 21 + 42 + 15 = 78.
Therefore the total number of ways of selecting the committee, while observing the restriction, is 1365 - 78 = 1287 ways.
Lucia made a mistake when she rewrote the formula
To rewrite the formula to x is a function of y. we have to add 2y to both sides of the formula. Instead of adding 2y, Lucia subtracted 2y from the right side.
Instead of what she did, x should be written the following way
The "rule of 72" says that the doubling time in years is approximately 72 divided by the interest rate in percent. To make the money grow by a factor of 4 requires that it double twice, so will take twice as long as the period to double once.
2×72/11.3 ≈ 12.7 . . . . years
_____
The "rule of 72" is an approximation. The actual quadrupling time for this interest rate and compounding is about 12.6 years. (The actual product of doubling time and nominal interest rate is about 71.25.)
4.5 thats the answer. Im just typing so its long enough blah blah blah
