Given: 7 different jellybeans
To Determine: How many ways the 7 different jellybeans can be lined up in a row of 3
Solution
We are considering an arrangement, so we would be using the permutation formula
The permuation formula is as shown below
[tex]_nP_r=\frac{n!}{(n-r)!}[/tex]Applying the formula above to the given as shown below
[tex]\begin{gathered} _7P_3=\frac{7!}{(7-3)!} \\ _7P_3=\frac{7\times6\times5\times4!}{4!} \\ _7P_3=7\times6\times5=210 \end{gathered}[/tex]Hence, the different ways 7 different jellybeans be lined up in a row of 3 is 210ways