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

Question

The number of permutations, of the digits 1 , 2 , 3 , &#8230; , 7 without repetition, which neither contain the string 153 nor the string 2467 , is _______ .

Quantrex Academy · Accepted Answer

Correct answer: 0

Given, The number 1 , 2 , 3 , . . . . , 7 Now total numbers of 7 digit number will be 7 ! without repetition, Now total numbers which contain string 154 will be 5 ! Total numbers which contain string 2367 will be 4 ! And number which contain both string 2367 &#160; &#38; &#160; 154 will be 2 So, total number which does not contain string 154 or 2367 will be 7 ! - 5 ! + 4 ! - 2 = 5040 - 120 + 24 - 2 = 5040 - 142 = 4898 Hence this is the required answer.

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

Correct answer

Step-by-step solution

More from Permutation and Combination

The number of permutations, of the digits 1 , 2 , 3 , &#8230; , 7 without repetition, which neither contain the string 153 nor the string 2467 , is _______ .

Correct answer

Step-by-step solution

More from Permutation and Combination

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