Question

1. - / 1 points

how many five - letter permutations can be formed from the first ten letters of the alphabet?
permutations
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1. - / 1 points

in how many ways can five students be seated in a row of five seats?
ways
resources
ebook

Explanation:

Step1: Define permutation formula

For permutations of $n$ items taken $k$ at a time: $P(n,k)=\frac{n!}{(n-k)!}$

Step2: Solve first problem (10 letters, 5-length)

$n=10, k=5$. Calculate $P(10,5)=\frac{10!}{(10-5)!}=10\times9\times8\times7\times6$
$10\times9\times8\times7\times6=30240$

Step3: Solve second problem (5 students, 5 seats)

$n=5, k=5$. Calculate $P(5,5)=\frac{5!}{(5-5)!}=5!$
$5!=5\times4\times3\times2\times1=120$

Answer:

1. 30240 permutations
2. 120 ways