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.