What a Lucky Blunder!

Hamza has bad handwriting and accidentally saw all the $+$ signs as $\times$ signs on his test. Luckily he still got the right answer! The first two problems were

$\begin{array} {rrcl} 1) & 2+2 & = & 2\times 2 \\ 2) & 1+2+3 & = &1\times 2 \times 3 \end{array}$

The problems continue to go on to the addition of $4$ numbers , $5$ numbers and so on. If Hamza got lucky again on the 4th problem, how many possibilities are there for his answer?

Note :Problems are ordered in ascending order of numbers added. All numbers are positive integers.