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 ((2m)!/(m!)2), if distinction is to be made between groups.

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 ((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.

Tardigrade Admin · Accepted Answer

Total objects = 6 1st kind (heads) = 3 2nd kind (Tails) = 3 ∴ Required ways = (6!/3!3!) = 20 ∴ Assertion (A) Reason (R) both are correct.

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true.

Total objects $= 6$
$1^{s t}$ kind (heads) $= 3$
$2^{n d}$ kind (Tails) $= 3$
$∴$ Required ways $= \frac{6 !}{3 ! 3 !} = 20$
$∴$ Assertion (A) & Reason (R) both are correct.

Both (A) & (R) are individually true & (R) is correct explanation of (A).

Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

(A) is true but (R) is false.

(A) is false but (R) is true.

Total objects =6 1st kind (heads) =3 2nd kind (Tails) =3 ∴ Required ways =3!3!6!​=20 ∴ Assertion (A) & Reason (R) both are correct.

Total objects $= 6$
$1^{s t}$ kind (heads) $= 3$
$2^{n d}$ kind (Tails) $= 3$
$∴$ Required ways $= \frac{6 !}{3 ! 3 !} = 20$
$∴$ Assertion (A) & Reason (R) both are correct.