Question

The number of permutations, of the digits 1, 2, 3, …..7 without repetition, which neither contain the string 153 nor the string 2467, is__.

Answer 1

Correct answer is 4898

Digits → 1, 2, 3, 4, 5, 6 , 7 

Total permutations = 7! 

Let A = number of numbers containing string 153 

Let B = number of numbers containing string 2467

n(neither string 153 nor string 2467) 

= Total – n(A ∪ B) 

= 7! – 142 = 4898