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Q.
Number of ways in which $21$ identical white balls and $19$ identical black balls be arranged in a row so that no $2$ black balls may be together is
Permutations and Combinations
Solution:
Let $x$ denote white balls then possible places for black balls are represented by '__'
As white balls are $21$ ,
$\Rightarrow$ possible places for blacks $(-)$ are $22$,
$\Rightarrow$ Number of selections for $19$ places for black balls from
$22$ possible places ${ }^{22} C_{19}$.
As all white balls are identical and all black balls are also identical, total number of arrangements $={ }^{22} C_{19}$
