Question

Six identical coins are arranged in a row. The total number of ways in which the number of heads is equal to the number of tails, is

• A. 9
• B. 20
• C. 40
• D. 120

Answer 1

The correct option is B 20

The required number of ways is the number of ways in which the letters
$HHHTTT$ can be arranged (H stands for heads while T stands for tails. Number heads= number of tails=given).
Hence they can be altogether arranged in 6! ways but, we have to account for 3 repetitive heads and tails
Thus, the required permutation is
$=\frac{6!}{3!3!}={}^6{C}_3=\frac{6\times 5\times 4}{3!}=20$.