geno3141

Process:  get all the variables ( the x's ) to one side, and all the number terms to the other.

Since the only number term is the  1  on the right side; leave it where it is and get rid of the  4x  term from the right side by subtracting  4x  from both sides:

    x  =  4x + 1

    x - 4x  =  4x - 4x + 1            (x - 4x  becomes  -3x)

    -3x  =  1                               (divide both sides by -1)

     x  =  -1/3

I see two parts to you question:

1)  If you want 2 men and 5 women, you wouldn't use 5C2;  5C2 represents the number of ways that you can        choose a set of 2 out of a set of 5;  this does not represent choosing 2 men and 5 women.

2)  Your formula:

     nCr  =  n! / [ r! · (n-r)! ]

     The  (n-r)!  in the denominator cancels all the factors in the numerator starting with (n-r) down through 1;        leaving only  n · (n-1) · (n-2) · ... · (n-r+2) · (n-r+1).

     There is still a factor of  r!  in the denominator.

     I agree with your process EXCEPT I feel that you need one fewer term in the numerator, because the (n-r)        factor gets cancelled also; in the numerator, stop with factor (n-r+1).

Let me modify my answer to represent having the plane hold 15 passengers:

The only way to overbook is for all 16 persons to show up; this will occur only if first persons shows up, the second person shows up, etc.

This has a probability of  (.94) x (.94) x ... x (.94)  all sixteen times, which is (.94)^16.

Find that value, that is the probability of having 16 out of 16 persons showing up.

I picture the question this way:

  outside, it is 69 degrees and every hour it goes up 2 degrees

  inside, it is 84 degrees and every hour it goes up 3 degrees,

then, when will the two temperatures be equal?

Never; outside starts lower than inside and outside increases by smaller amounts than inside:

outside:  69,  71,  73,  75,  ...

inside:    84,  87,  90,  93,  ...        The temperatures get further and further apart.

If you have a calculator that handles combinations  --  that is, you can calculate expressions such as 16C3, the combinational value of 16 items taken 3 at a time  --  you can do it like this:

The probability of having enough space is calculated as follows:

16C0 · (.94)^0 · (.06)^16                                (nobody shows up)

16C1 · (.94)^1 · (.06)^15                                (1 person shows up)

16C2 · (.94)^2 · (.06)^14                                (2 persons show up)

16C3 · (.94)^3 · (.06)^13                                (3 persons show up)

16C4 · (.94)^4 · (.06)^12                                (4 persons show up)

16C5 · (.94)^5 · (.06)^11                                (5 persons show up)

Sum these  6  values; this will give you the probability that everyone gets seated.

Overbooking would be the opposite, so subtract that answer from  1.000,  to get the probability that overboooking occurs. 

A simple interest problem is the type where you borrow the $28,000.00 at 1.7% and you are to pay it all back in one payment in three years.

For this type problem, use the formula;  i  =  prt,

where  i  represents the amount of interest owed                (what you want to figure out)

          p  represents the principal (amount borrowed)           ($28,000.00

          r  represents the interest rate, as a decimal               (1.7%  =  0.017)

          t  represents the time                                              (3 years)

  i  =  Prt   ===>   i  =  (28000)(.017)(3)   ===>  i  =  $1428.00

So, you will have to pay back the original amount, $28000.00, plus the interest earned, $1428.00, for a total of   $29,428.00.

(This assumes that you make no month payments, or any other complication.)

We will need to figure what number times the length of each side will give us the right perimeter.

Call this number  x,  and multiply it times each side, so now the sides are  8x,  7x,  and 5x.

If we add the sides togeter, we get the perimeter:

Perimeter  =  8x + 7x + 5x

     240      =  8x + 7x + 5x

     240      =  20x

       12      =  x

8x becomes 8(12) = 96

7x becomes 7(12) = 84

5x becomes 5(12) = 60          and 96 + 84 + 60 = 240

It's an expression and can't (really) be simplified.

         Distance = Rate x Time

            13m    =  (2.1 m/s) x Time                       Divide both sides by 2.1:

13m / 2.1 m/s  =  Time

    6.2 seconds  =  Time  (approximately)

This type of question will not have a specific numerical answer.