Question

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

• A. ${}^{21}{C}_{18}$
• B. ${}^{22}{C}_{19}$
• C. ${}^{20}{C}_{17}$
• D. None of these

Answer 1

Answer: (B)

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 $={}^{22}{C}_{19}$