Question

A "child has six blocks, three of which are red and three of which are green". How many patterns can shemake by placing them all in a line?If she is given threewhite blocks, how many total patterns can she make by placing all nine blocks in a line?

Answer 1

Answer: There are 20 ways and 1680 ways respectively.

Step-by-step explanation:

Since we have given that

Total number of blocks = 6

Number of red blocks = 3

Number of green blocks = 3

So, Number of patterns she can make by placing them all in a line is given by

$\dfrac{6!}{3!\times 3!}\\\\=20$

If there are 3 white blocks

so, total number of white blocks becomes 9

So, Number of total pattern she can make by placing all nine blocks in a line is given by

$\dfrac{9!}{3!\times 3!\times 3!}\\\\=1680\ ways$

Hence, there are 20 ways and 1680 ways respectively.