Answer:
Part 1: There are 4.7*10^21 ways to select 40 volunteers in subgroups of 10
Part 2: The research board can be chosen in 32760 ways
Step-by-step explanation:
Part 1:
The number of ways in which we can organized n elements into k groups with size n1, n2,...nk is calculate as:

So, in this case we can form 4 subgroups with 10 participants each one, replacing the values of:
- n by 40 participants
- k by 4 groups
- n1, n2, n3 and n4 by 10 participants of every subgroups
We get:

Part 2:
The number of ways in which we can choose k element for a group of n elements and the order in which they are chose matters is calculate with permutation as:

So in this case there are 4 offices in the research board, those are director, assistant director, quality control analyst and correspondent. Additionally this 4 offices are going to choose from a group of 5 doctors.
Therefore, replacing values of:
- n by 15 doctors
- k by 4 offices
We get:

So the ratio is 1 to 2 to 5
so basically 1 unit of soda water to 2 units of fruit punch to 5 units of ginger ale
total is 1+2+5=8 units
so 4 gallons=8 units
divide by 8
1/2 gallon=1 unit
soda water=1 unit=1/2 gallon
fruit punch=2 unit=1/2 times 2=1 gallon
ginger ale=5 unit=5 times 1/2=5/2=2 and 1/2 gallon
soda water=1/2 gallon
fruit punch concentrate=1 gallon
ginger ale=5/2 gallon or 2 and 1/2 gallon
Answer:
David needs 36.style="color:rgb(72,72,72);background-color:transparent;"> gallons of punch for a party and has two different coolers to carry it in. The bigger cooler is 5. times as large as the smaller cooler.
Answer:
Step-by-step explanation:
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