Answer:
There are 165 ways to distribute the blackboards between the schools. If at least 1 blackboard goes to each school, then we only have 35 ways.
Step-by-step explanation:
Essentially, this is a problem of balls and sticks. The 8 identical blackboards can be represented as 8 balls, and you assign them to each school by using 3 sticks. Basically each school receives an amount of blackboards equivalent to the amount of balls between 2 sticks: The first school gets all the balls before the first stick, the second school gets all the balls between stick 1 and stick 2, the third school gets the balls between sticks 2 and 3 and the last school gets all remaining balls.
The problem reduces to take 11 consecutive spots which we will use to localize the balls and the sticks and select 3 places to put the sticks. The amount of ways to do this is 
As a result, we have 165 ways to distribute the blackboards.
If each school needs at least 1 blackboard you can give 1 blackbooard to each of them first and distribute the remaining 4 the same way we did before. This time there will be 4 balls and 3 sticks, so we have to put 3 sticks in 7 spaces (if a school takes what it is between 2 sticks that doesnt have balls between, then that school only gets the first blackboard we assigned to it previously). The amount of ways to localize the sticks is 
. Thus, there are only 35 ways to distribute the blackboards in this case.
Because the ratio of yellow to blue can be expressed as 5/3, you would solve the equation 5/3= 2/x. To solve, you would get x alone by cross multiplying and getting 5x=6. Divide both sides by 5 and get 6/5 or 1 and 1/5 cans of blue paint
Answer:
Part A:
Part B:
Generations Age=25*39=975 years
Part C:
- Some ancestors on different branches of the family tree must be the same.
- There could not have been 39 generations in my line of ancestry.
Step-by-step explanation:
Given Data:
Two Parents, Four Grand Parents, Eight great Grand Parents.
Generation=39
Solution:
Part A:
From given data Following series is made:
Now, Above series will become:
![2[1+2+2^2+......+2^{38}]](https://tex.z-dn.net/?f=2%5B1%2B2%2B2%5E2%2B......%2B2%5E%7B38%7D%5D)
From geometric Sequence:
![2[\frac{2^{38+1}-1}{2-1} ]](https://tex.z-dn.net/?f=2%5B%5Cfrac%7B2%5E%7B38%2B1%7D-1%7D%7B2-1%7D%20%5D)
Part B:
Generations Age=years*Number of generations
Generations Age=25*39=975 years
Part C:
Number of people lived= 10^11
Ancestors=
It means ancestors are not distinct, it means:
- Some ancestors on different branches of the family tree must be the same.
- There could not have been 39 generations in my line of ancestry.
Notice that 25+23+17+14+12+9=100, so among these students there are no 2 studying 2 subjects.
The probabilities of selecting students studying a certain subject are as follows
P(physics)=25/100
P(chemistry)=17/100
P(maths)=9/100
P(sociology)=23/100
P(political sciences)=14/100
P(anthropology)=12/100
since all the sets are disjoint, that is there are no common elements, and since all the students in consideration are enrolled in one these 6 subjects:
P(physics)+P(chemistry)+P(maths)+P(sociology)+P(political sciences)
+P(anthropology)=1
P(a)=P(sociology)+P(political sciences)+P(anthropology)+P(physics)
thus
P(a')=1-P(a)=P(chemistry)+P(maths)=17/100+9/100=26/100=0.26
Answer: 0.26
