Question

Assertion A : The number of ways in which 3 married couples with their 4 children can sit in a row such that no husband and wife are together, are 10! - 3. 9! + 3. 8! - 7!. Reason R : Number of ways of occurrence of at least one event out of three events A, B & C = n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(C∩A) + n(A∩B∩C).

• A. Both A and R are correct but R is NOT the correct explanation of A
• B. Both A and R are correct and R is the correct explanation of A
• C. A is correct but R is not correct
• D. A is not correct but R is correct

Answer 1

Answer: (D)

A is not correct but R is correct

Answer 2

The assertion is incorrect because it misses factors of 2 in the Inclusion-Exclusion Principle calculation. The correct count using Inclusion-Exclusion should be:

$$10! - 3(2 \cdot 9!) + 3(2^2 \cdot 8!) - (2^3 \cdot 7!)$$

The given assertion is:

$$10! - 3 \cdot 9! + 3 \cdot 8! - 7!$$

The reason (R) provides the standard Inclusion-Exclusion formula for three events, which is correct. However, it doesn't directly explain why assertion A is wrong.