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Suppose we want to choose 5 letters, without replacement, from 16 distinct letters.(a) If the order of the choices is taken into consideration, how many ways can this be done?0(b) If the order of the choices is not taken into consideration, how many ways can this be done?

Respuesta :

Explanation:

a) Given: Order is important and replacement is not allowed.

This is a permutation.

Number of ways =

[tex]\begin{gathered} N\text{ = }\frac{n!}{(n-r!)} \\ N\text{ = }\frac{16!}{(16-5)!} \\ \text{ =524160} \end{gathered}[/tex]

Answer: 524160

b) Order is not important, replacement is not allowed.

This is a combination.

[tex]\begin{gathered} N\text{ = }\frac{n!}{(n-r)!*r!} \\ N\text{ = }\frac{16!}{(16-5)!*5!} \\ N\text{ = 4368} \end{gathered}[/tex]

Answer: 4

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