Question

Suppose the sample space for a probability experiment has 8 elements. If elements from the sample are selected without replacement, how many different ways can you select all of them? Remember that "without replacement" means that the items are not returned to the sample space after they are chosen. Write your answer in factorial notation.

Answer 1

Answer: Number of ways $=\dfrac{8!}{8!0!}\ or \ 1$

Step-by-step explanation:

When there is no replacement , we use combination to find the number of ways to choose things.

Number of ways to choose r things out of  ( with out replacement) = $^nC_r=\dfrac{n!}{r!(n-r)!}$

The number of ways to choose  8 things = $^8C_8=\dfrac{8!}{8!(8-8)!}=\dfrac{1}{0!}=1 [\because 0!=1]$

Hence,  Number of ways $=\dfrac{8!}{8!0!}\ or \ 1$