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Chapter 1: Q.1.9 (page 15)

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 ?

Short Answer

Expert verified

Total possible arrangements are 27720

Step by step solution

01

.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

02

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 12!6!4!1!1!=12脳11脳10脳9脳8脳7脳6!4脳3脳2脳1脳6!=27720

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