Originally Posted by

**Soroban** Hello, Masterthief1324!

I agree with skeeter and Dinkydoe . . .

. . $\displaystyle \begin{array}{ccccc}$$\displaystyle

\text{1-at-a-time:} & _5C_1 &=& 5 \\

\text{2-at-a-time:} & _5C_2 &=& 10 \\

\text{3-at-a-time:} & _5C_3 &=& 10 \\

\text{4-at-a-time:} & _5C_4 &=& 5 \\

\text{5-at-a-time:} & _5C_5 &=& 1 \\ \hline

& \text{Total:} && {\color{blue}31}

\end{array}$

Call the five basic tastes: $\displaystyle a,b,c,d,e$

You can list them and count them yourself . . .

. . $\displaystyle \begin{array}{ccc}\text{1-at-a-time:} & a,b,c,d,e \\ \\$$\displaystyle

\text{2-at-a-time:} & ab,ac,ad,ae,bc\\

& bd,be,cd, ce, de \\ \\

\text{3-at-a-time:} & abc, abd, abe, acd, ace \\

& ade, bcd, bce, bde, cde \\ \\

\text{4-at-a-time:} & abcd, abce, abde, acde, bcde \\ \\

\text{5-at-a-time:} & abcde

\end{array}$