Question

There are 11 candidates for three postions at a restaraunt. One postion is for a cook. The second position is for a food server The third position is for a cashier If all 11 candidates are equally qualfied for the theee positions, in how many diflerent ways can the three postions be Sted? diferent ways to fil the three posilions There ate 19 pm Emer your anwer in the atcwer box Cameten Netecr Desitu La-rie Kensington 8 c 5 3 Eng PuD Eter

Answer 1

Answer:

165 combinations possible

Step-by-step explanation:

This is a combination problem as opposed to a permutation, because the order in which we fill these positions is not important.  We are merely looking for how many ways each of these 11 people can be rearranged and matched up with different candidates, each in a different position each time.  The formula can be filled in as follows:

₁₁C₃ = $\frac{11!}{3!(11-3)!}$

which simplifies to

₁₁C₃ = $\frac{11*10*9*8!}{3*2*1(8!)}$

The factorial of 8 will cancel out in the numerator and the denominator, leaving you with

₁₁C₃ = $\frac{990}{6}$

which is 165