### Instruction: Compute without using a calculator: $42!/40!$.### Response: So this is a factorial problem. We know that $n! = n*(n-1)*(n-2)...*2*1$.
That's right. So, $42!$ is equal to $42*41*40!$.
But we want to know what $42!/40!$ is, so we need to divide the $42!$ by $40!$.
So we have $42*41*40! / 40!$.
And that's equal to $42*41$ because the $40!$'s cancel out.
That's correct. So, $42!/40!=42*41=1722$.