Permutations & Combinations
Permutations Avoiding Given Strings
nta_pyq_2023_apr
Grade 11
Question:
Number of permutations of 1,2,3,…,7 without repetition, containing neither string 153 nor 2467, is _______.
Step-by-Step Solution
Key Concept: Total $=7!$. $|A|$ (contains 153) $=5!$. $|B|$ (contains 2467) $=4!$. $|A\cap B|$ (contains both) $=2!$. Inclusion-exclusion: $|A\cup B|=5!+4!-2!$.
$5040-120-24+2=4898$.
Correct Answer: 4898