Home Maths Permutations & Combination JEE Main 2023 The number of permutations, of the digits 1,…
Maths Permutations & Combination JEE Main 2023 Numeric Response
Published on: August 14, 2026

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

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The correct answer is:
4898

(4898)

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 & 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

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