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Lunna [17]
3 years ago
7

The economics department has 40 applicants for their phd program and only 10 openings. how many different combinations of applic

ants admitted into the program are possible?
Mathematics
1 answer:
lana66690 [7]3 years ago
5 0

In a sequence of events, the total possible number of ways all events can performed is the product of the possible number of ways each individual event can be performed. Since there are 10 openings

<span>P = 40 x 39 x 38 x 37 x 36 x 35 x 34 x 33 x 32 x 31 = 3.07599 x 10^15 different combinations</span>

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Fill in each slot in the square with variables <em>a</em>, <em>b</em>, <em>c</em>, <em>d</em>, and <em>e</em>, in order from left-to-right, top-to-bottom. In a magic square, the sums across rows, columns, and diagonals all add up to the same number called the <em>magic sum</em>.

The magic sum is -3.9, since "diagonal 2" (bottom left to top right) has all the information we need:

3 + (-1.3) + (-5.6) = -3.9

Use this to find the remaining elements

  • row 1:

<em>a</em> + <em>b</em> + (-5.6) = -3.9

  • row 2:

<em>c</em> + (-1.3) + <em>d</em> = -3.9

  • row 3:

3 + <em>e</em> + 0.02 = -3.9

  • column 1:

<em>a</em> + <em>c</em> + 3 = -3.9

  • column 2:

<em>b</em> + (-1.3) + <em>e</em> = -3.9

  • column 3:

(-5.6) + <em>d</em> + 0.02 = -3.9

  • diagonal 1 (top left to bottom right):

<em>a</em> + (-1.3) + 0.02 = -3.9

You will find

<em>a</em> = -2.62

<em>b</em> = 4.32

<em>c</em> = -4.28

<em>d</em> = 1.68

<em>e</em> = -6.92

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