The number of different ways to distribute m indistinguishable balls into n
distinguishable urns is given by C(m+n-1,n-1).
For example, the number of ways 6 ball can be placed in 7 boxes is given by C(6+7-1, 7-1) = C(12, 6) = 924 ways.
Answer:
Option D is correct.
Explanation:
Commutative Property of Multiplication define that two numbers can be multiplied in any order.
i.e
Distributive property of multiplication states that when a number is multiplied by the sum of two numbers i.e, the first number can be distributed to both of those numbers and multiplied by each of them separately.
![a \times (b+c) = a\times b+ a\times c](https://tex.z-dn.net/?f=a%20%5Ctimes%20%28b%2Bc%29%20%3D%20a%5Ctimes%20b%2B%20a%5Ctimes%20c)
Associative property of multiplication states that multiplication allows us to group factors in different ways to get the same product.
Given:
A = ![( 4\times 3) + (2 \times 4 )= ( 4\times 3) + (4 \times 2 )](https://tex.z-dn.net/?f=%28%204%5Ctimes%203%29%20%2B%20%282%20%5Ctimes%204%20%29%3D%20%28%204%5Ctimes%203%29%20%2B%20%284%20%5Ctimes%202%20%29)
B = ![4 \times ( 3+2)](https://tex.z-dn.net/?f=4%20%5Ctimes%20%28%203%2B2%29)
C = ![4 \times 5](https://tex.z-dn.net/?f=%204%20%5Ctimes%205)
then;
![( 4\times 3) + (2 \times 4 )](https://tex.z-dn.net/?f=%28%204%5Ctimes%203%29%20%2B%20%282%20%5Ctimes%204%20%29)
Using Commutative property of Multiplication we can write
then we have;
![( 4\times 3) + (2 \times 4 ) = ( 4\times 3) + (4 \times 2 )](https://tex.z-dn.net/?f=%28%204%5Ctimes%203%29%20%2B%20%282%20%5Ctimes%204%20%29%20%3D%20%28%204%5Ctimes%203%29%20%2B%20%284%20%5Ctimes%202%20%29)
Using Distributive property of multiplication;
![( 4\times 3) + (4 \times 2 ) = 4 \times ( 3+2)](https://tex.z-dn.net/?f=%28%204%5Ctimes%203%29%20%2B%20%284%20%5Ctimes%202%20%29%20%3D%204%20%5Ctimes%20%28%203%2B2%29)
by using associative property of multiplication ,
![4 \times (3+2) = 4 \times 5](https://tex.z-dn.net/?f=4%20%5Ctimes%20%283%2B2%29%20%3D%204%20%5Ctimes%205)
Therefore, the reasons for A , B and C in this proof are;
A.commutative property of multiplication
B. distributive property
C. associative property of multiplication
Answer:
you can use a website called wolfram alpha to help with any math equation
Step-by-step explanation:
Answer:
c
Step-by-step explanation:
I am not sure