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  4. The tensdigit of 1 !+2 !+3 !+ ldots+49 ! is

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Q. The tensdigit of $1 !+2 !+3 !+\ldots+49 !$ is

Permutations and Combinations

Solution:

We know that $1 !+2 !+3 !+4 !=33$.
Also, $5 !=120,6 !=720,7 !=5040,8 !=40320$ and $9 !=362880$.
Thus, tens digit of $1 !+2 !+\ldots+9 !$ is $1$ .
Also, note that $n !$ is divisible by $100$ for all $n \geq 10$.
Therefore, the tens digit of $1 !+2 !+\ldots+49 !$ is $1$