Question

In how many ways can $21$ white and $19$ black balls be put in a row so that no two black balls are together?

• A. $1470$
• B. $1540$
• C. $735$
• D. $Noneofthese$

Answer 1

The correct option is B $1540$

Let us first keep the 21 white balls in a row.

Now there are 22 positions in which the black balls can be accommodated (including between white balls and at the ends).

No. of ways = ${}^{22}{C}_{19}=1540$