question 3 of 6
declan has 100 songs on his playlist. he is going for a run and has time to listen to 8 songs while he runs. declan decides to use the random shuffle feature to determine which songs will play, and in what order. (the random shuffle feature does not allow any song to be played twice.)
how many different lists of 8 songs are possible?
express your answer in scientific notation.
round the first number to one decimal place. enter the correct exponent on the \10^\. ×10

Question

Accepted Answer

# Explanation:
## Step1: Identify the permutation formula
The number of permutations of $n$ objects taken $r$ at a time is $P(n,r)=\frac{n!}{(n - r)!}$. Here $n = 100$ and $r=8$.
## Step2: Calculate $P(100,8)$
$$
\begin{align*}
P(100,8)&=\frac{100!}{(100 - 8)!}\
&=\frac{100!}{92!}\
&=100\times99\times98\times97\times96\times95\times94\times93\
\end{align*}
$$
$$
\begin{align*}
100\times99& = 9900\
9900\times98&=970200\
970200\times97& = 94109400\
94109400\times96&=9034502400\
9034502400\times95&=858277728000\
858277728000\times94&=80678106432000\
80678106432000\times93&=7.503063898176\times10^{15}
\end{align*}
$$

# Answer:
$7.5\times 10^{15}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Identify the permutation formula

Step2: Calculate \(P(100,8)\)

Answer: