Question

Assertion (A) : Six identical coins are arranged in a row, the number of ways in which the number of heads is equal to the number of tails is $20$.
Reason (R) : The number of ways in which $2m$ different things can be divided into two groups containing $m$ things in each group is $\frac{(2m)!}{(m!)^2}$, if distinction is to be made between groups.

• A. Both (A) & (R) are individually true & (R) is correct explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

Total objects $= 6$
$1^{st}$ kind (heads) $= 3$
$2^{nd}$ kind (Tails) $= 3$
$\therefore $ Required ways $ = \frac{6!}{3!3!} = 20$
$\therefore $ Assertion (A) & Reason (R) both are correct.