Respuesta :
Answer:
5040 ways
Step-by-step explanation:
Since there are 10 blocks,
It can be arranged in 10! ways
But there is 5 green,3 red, 1 white and 1 black blocks.
Therefore, the blocks can be arranged in 10!/(5!*3!*1!*1!) ways
= 5040 ways
There are 5040 ways of possible arrangements, If we put the blocks in a line.
Given that,
We have 10 blocks, of which 5 are green, 3 are red, 1 is white, and 1 is black.
We have to determine,
If we put the blocks in a line, how many arrangements are possible?
According to the question,
Total number of blocks = 10
Number of green blocks = 5
Number of red blocks = 3
Number of white blocks = 1
Number of black blocks = 1
Then,
If we put the blocks in a line, the number of possible arrangements is,
[tex]\rm Number \ of \ possible \ arrangement = \dfrac{Total \ number \ of \ blocks}{ Green \times red \times black \times \ white }[/tex]
Substitute all the values in the formula,
[tex]\rm Number \ of \ possible \ arrangement = \dfrac{10!}{ 5!\times 3! \times 1! \times \ 1! }\\\\ Number \ of \ possible \ arrangement =\dfrac{3628800}{120 \times 6 \times 1\times1 }\\\\ Number \ of \ possible \ arrangement =5040[/tex]
Hence, there are 5040 ways of possible arrangements, If we put the blocks in a line.
For more details refer to the link given below.
https://brainly.com/question/11732255
