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Vesnalui
2 months ago
14

A 20-person fraternity is making their weekend plans around 5 different parties in IV. Each brother will attend exactly one of t

he parties. Fraternity rules state that the fraternity must have a representative at each party. Assume that only the number of brothers that show up at a party is important, i.e. the brothers are indistinguishable. (a) How many different arrangements of plans are possible
Mathematics
1 answer:
Leona [12.6K]2 months ago
3 0

Answer:

3876

Step-by-step explanation:

We have the following data:

Members of the fraternity = 20

Their attendance at five parties is organized into groups of four.

This indicates that each group consists of 4 individuals.

At least one brother will be present at exactly one of the gatherings. (The brothers are indistinguishable).

Thus, precisely one brother at a gathering leaves (20 - 1) = 19, due to their indistinct nature.

Group sizes are in fours.

Calculating 19C4:

From: nCr = n! /(n-r)! r!

19C4 = 19! / (19 - 4)! 4!

= 19! / 15! 4!

= (19 * 18 * 17 * 16) / (4 * 3 * 2)

= 93024 / 24

= 3876

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Step 1:

Set the compass to a distance greater than half the length of segment AB, place it on point A, and draw an arc across AB.

Step 2:

Keeping the same width, place the compass on point B and create another arc across AB.

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