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

3876

Step-by-step explanation:

Given the following :

Fraternity members = 20

They are to attend 5 different parties in groups of 4

Meaning a group = 4 persons

Atleast one brother will attend exactly one of the parties. (the brothers are indistinguishable).

Then, exactly one brother at a party (20 - 1) = 19, since they are indistinguishable.

Group members are in 4's

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

725 parts per hour.

step-by-step explanation:

hi there, this answer is actually really simple.

you can set it up as 1450/2 or 3625/5 to find the answer.

they want to know how much per hour is being made, so you just divide.

1450/2=725.

and that's how many are produced per hour.

hope this . : )

7 weeks

step-by-step explanation:

convert each fraction to the least common multiple of 20, so 3/4 = 15/20 & 1/10 = 2/20, then divide 15 by 2 and you get a little over 7, so the food will last 7 weeks.