MATH MAGIC

Pythagoras Is No Longer A Dinosaur
Make Your Concepts

    Consider two different types of arrangements :
    1. Arrangements of  n  white balls and any number of black balls out of  m  black balls (the number of black balls may be zero also).
    2. Arrangements of  n + 1  white balls and  m  black balls taken all at a time.

    Look !  You will find below that there is one to one correspondence between these two types of arrangements. Is not it an interesting relation ?  Definitely it is.
    Consider “Arrangements of 2 white balls and any number of black balls out of 2 black balls.” There are three mutually exclusive and exhaustive hypotheses:
    (i)    Only 2 white balls are arranged. The arrangement is  WW.
    (ii)    2 white balls and 1 black ball are arrangement. The arrangements are      WWB, WBW,  BWW.
    (iii)    2 white and 2 black balls are arranged. The arrangements are  WWBB, WBWB, WBBW,  BWWB,  BWBW,  BBWW.
   
    Now let us look at the correspondence between the above arrangements and the arrangements of (2+1) white and 2 black taken all at a time.