Q.1.9 - A First Course in Probability

Question

A child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. If the child puts the blocks in a line, how many arrangements are possible ? 

Step-by-Step Solution

Answer

Total possible arrangements are 27720

Step 1 .Given information

Here a child has 12 blocks, of which 6 are black, 4 are red, 1 is white, and 1 is blue. we have to find the possible arrangement if the child puts the blocks  in a line 

Step 2. finding the arrangements if the child put the blocks in a line

 If the child puts the 12 blocks in a line, then the different possible arrangements and from 12 blocks 6 are blacks means  6blocks  are identical and 4 are red so 4 identical red blocks is the there and there is white and 1 blue block are there, .To get a different arrangement we have to divide 12! by identical arrangements .thus the arrangements will be  $$\begin{gathered} \frac{12!}{6!4!1!1!}=\frac{12\times 11\times 10\times 9\times 8\times 7\times 6!}{4\times 3\times 2\times 1\times 6!} \\ =27720 \end{gathered}$$