Respuesta :
Answer:
There are 8568 ways to combine the shoes.
Step-by-step explanation:
In this case Connie wants to create smaller subsets from a larger group of things, therefore we must do a combination, which can be applied by using the following formula:
[tex]C_{(n,r)} = \frac{n!}{r!*(n - r)!}[/tex]
In our case n = 18, which is the total number of shoes and r = 5, which is the subset she wants to create.
[tex]C_{(18,5)} = \frac{18!}{5!*(18 - 5)!} = \frac{18!}{5!*13!} = \frac{18*17*16*15*14*13!}{5!*13!}\\C_{(18,5)} = \frac{18*17*16*15*14}{5*4*3*2} = 8568[/tex]
There are 8568 ways to combine the shoes.
The number of ways can she choose which shoes to take is 8,568.
Given that,
- Connie is packing for a trip. She has 18 pairs of shoes and she has room to pack 5 pairs.
Based on the above information, the calculation is as follows:
[tex]= \frac{n!}{k!(n-k)!} \\\\= \frac{18!}{5!13!} \\\\= \frac{18\times 17\times 16\times\15\times \times 14}{5\times 4\times 3\times2\times 1}[/tex]
= 8,568
Therefore we can conclude that The number of ways can she choose which shoes to take is 8,568.
Learn more: brainly.com/question/17429689
