Question

For a segment of a radio show, a disc jockey can play 8 records. If there are 10 records to select from, in how many ways can the program for this segment bearranged?ways

Answer 1

Since the question is asking for the order of arrangement, we will use permutation.

There are 8 records that can be picked from 10 records. Therefore, we can find the number of ways of selection is given as

$^{10}P_8$

Using the permutation formula, we have

$^{10}P_8=\frac{10!}{(10-8)!}$

Solving, we have

$\begin{gathered} ^{10}P_8=\frac{10\times9\times8\times7\times6\times5\times4\times3\times2\times1}{2\times1} \\ ^{10}P_8=1814400 \end{gathered}$

Therefore, there are 1,814,400 ways for the segment to be arranged.