The remainderwhen  1! + 2! + 3! + …+ 20!15 Select an answerA4B3C5D7

The question is asking for the remainder when the sum of the factorials from 1 to 20 is divided by 15.

The factorial of a number n, denoted as n!, is the product of all positive integers less than or equal to n.

Let's calculate the factorials from 1 to 20 and their remainders when divided by 15:

1! = 1, remainder when divided by 15 is 1 2! = 2, remainder when divided by 15 is 2 3! = 6, remainder when divided by 15 is 6 4! = 24, remainder when divided by 15 is 9 5! = 120, remainder when divided by 15 is 0 6! = 720, remainder when divided by 15 is 0 7! = 5040, remainder when divided by 15 is 0 8! = 40320, remainder when divided by 15 is 0 9! = 362880, remainder when divided by 15 is 0 10! = 3628800, remainder when divided by 15 is 0 11! = 39916800, remainder when divided by 15 is 0 12! = 479001600, remainder when divided by 15 is 0 13! = 6227020800, remainder when divided by 15 is 0 14! = 87178291200, remainder when divided by 15 is 0 15! = 1307674368000, remainder when divided by 15 is 0 16! = 20922789888000, remainder when divided by 15 is 0 17! = 355687428096000, remainder when divided by 15 is 0 18! = 6402373705728000, remainder when divided by 15 is 0 19! = 121645100408832000, remainder when divided by 15 is 0 20! = 2432902008176640000, remainder when divided by 15 is 0

From 5! onwards, all the factorials are divisible by 15, so their remainders are 0.

So, we only need to consider the sum of the remainders from 1! to 4!, which is 1 + 2 + 6 + 9 = 18.

When 18 is divided by 15, the remainder is 3.

So, the answer is B3.