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  • The number of permutations of the digits 1, 2, 3, ...., 7 without repetition, which neither contain the string 153 nor the string 2467, is _____.Option: 1

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

Option: 1

4898


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

Numbers are 1, 2, 3, 4, 5, 6, 7
Numbers having string (154) = (154), 2, 3, 6, 7 = 5!
Numbers having string (2467) = (2467), 1,3, 5 = 4!
Number having string (154) and (2467)
= (154), (2467) = 2!
Now n (154 \cup 2467) = 5! + 4! – 2!
= 120 + 24 – 2 = 142
Again total numbers = 7! = 5040
Now required numbers = n (neither 154 nor 2467)
= 5040 – 142
= 4898

Posted by

Suraj Bhandari

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