using a red, blue, green and yellow block only once in each row, how many four block patterns can you make that have a red block in the first position?

Answer:6 waysStep-by-step explanation:The number of ways in which [tex]n[/tex] distinct objects can be arranged in  a row is [tex]n![/tex].[tex]n![/tex][tex]=n\times (n-1)\times (n-2).......\times 2\times 1[/tex]Given that we have [tex]4[/tex] distinct blocks and each block can be used only once.We need four block patterns which means we need all all the four blocks available to creating one pattern.Given that every pattern starts with a red block.So,three blocks can be arranged after the red block in [tex]3![/tex] ways.So,the number of patterns that can be made is [tex]6[/tex].