The remainder when x = 1 ! + 2 ! + 3 ! + 4 ! + … .. + 100 ! is divided by 240 , is

For r ≥ 6 , r ! is divisible by 240. ∴ remainder = 1 ! + 2 ! + 3 ! + 4 ! + 5 ! = 153

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MathematicsPermutation & CombinationFundamental PrincipleEasy2 minQB

MathematicsEasysingle choice

The remainder when $x = 1! + 2! + 3! + 4! + \dots .. + 100$ ! is divided by 240 , is

Answer:

Solution:

For $r \geq 6, r!$ is divisible by 240.

$∴ remainder = 1! + 2! + 3! + 4! + 5! = 153$

Stream:JEESubject:MathematicsTopic:Permutation & CombinationSubtopic:Fundamental Principle

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