. 7 prizes are to be distributed between 3 people with a guarantee that each person gets at least one prize. Find the number of
1 answer:
Answer:
Total number of ways to distribute the prize = 2187
Step-by-step explanation:
Given:
Number of prizes = 7
Number of peoples = 3
We need to find the total number of ways to distribute the prize.
Solution:
From the above statement, 7 prizes are to be distributed between 3 people, wherein each person gets at least one prize.
Each prize is to be distributed among three persons. When the first prize is to be awarded, one of the three is chosen to win the prize. When the second prize is to be awarded, there are again three choices.
So, total number of distribution of the prizes is given as:
Therefore, total number of ways to distribute the prizes = 2187
You might be interested in
Answer:
Remember, if B is a set, R is a relation in B and a is related with b (aRb or (a,b))
1. R is reflexive if for each element a∈B, aRa.
2. R is symmetric if satisfies that if aRb then bRa.
3. R is transitive if satisfies that if aRb and bRc then aRc.
Then, our set B is .
a) We need to find a relation R reflexive and transitive that contain the relation
Then, we need:
1. That 1R1, 2R2, 3R3, 4R4 to the relation be reflexive and,
2. Observe that
- 1R4 and 4R1, then 1 must be related with itself.
- 4R1 and 1R4, then 4 must be related with itself.
- 4R1 and 1R2, then 4 must be related with 2.
Therefore is the smallest relation containing the relation R1.
b) We need a new relation symmetric and transitive, then
- since 1R2, then 2 must be related with 1.
- since 1R4, 4 must be related with 1.
and the analysis for be transitive is the same that we did in a).
Observe that
- 1R2 and 2R1, then 1 must be related with itself.
- 4R1 and 1R4, then 4 must be related with itself.
- 2R1 and 1R4, then 2 must be related with 4.
- 4R1 and 1R2, then 4 must be related with 2.
- 2R4 and 4R2, then 2 must be related with itself
Therefore, the smallest relation containing R1 that is symmetric and transitive is
c) We need a new relation reflexive, symmetric and transitive containing R1.
For be reflexive
- 1 must be related with 1,
- 2 must be related with 2,
- 3 must be related with 3,
- 4 must be related with 4
For be symmetric
- since 1R2, 2 must be related with 1,
- since 1R4, 4 must be related with 1.
For be transitive
- Since 4R1 and 1R2, 4 must be related with 2,
- since 2R1 and 1R4, 2 must be related with 4.
Then, the smallest relation reflexive, symmetric and transitive containing R1 is
Answer: Second option.
Step-by-step explanation:
It is important to remember the Distributive Property in order to solve this exercise.
The Distributive property states that:
In this case you have the following expression provided in the exercise:
Then, in order to write this expression in another way, you can apply the Distributive property. Multiply each number inside the parentheses by "t".
Applying this procedure, you get:
Notice that this expression matches with the one shown in the the second option.