How many ways can 5 people be arranged in a line?
1 answer:
Answer: 120 ways
Step-by-step explanation: In this problem, we're asked how many ways can 5 people be arranged in a line.
Let's start by drawing 5 blanks to represent the 5 different positions in the line.
Now, we know that 5 different people can fill the spot in the first position. However, once the first position is filled, only 4 people can fill the second spot and once the second spot is filled, only 3 people can fill the third spot and so on. So we have <u>5</u> <u>4</u> <u>3</u> <u>2</u> <u>1</u>.
Now, based on the counting principle, there are 5 x 4 x 3 x 2 x 1 ways for all 5 spots to be filled.
5 x 4 is 20, 20 x 3 is 60, 60 x 2 is 120, and 120 x 1 is 120.
So there are 120 ways for all 5 spots to be filled which means that there are 120 ways that 5 people can be arranged in a line.
I have also shown my work on the whiteboard in the image attached.
You might be interested in
Answer:
There is no enough evidence to support the claim that the proportion of US teens that have some level of hearing loss differs from 20%.
P-value=0.12
Step-by-step explanation:
We have to perform a test of hypothesis on the proportion.
The claim is that the proportion of US teens that have some level of hearing loss differs from 20%.
Then, the null and alternative hypothesis are:
The significance level is assumed to be 0.05.
The sample, of size n=1981, has 369 positive cases. Then, the proportion is:
The standard error of the proportion is:
Now, we can calculate the statistic z:
The P-value for this two-tailed test is:
The P-value is below the significance level, so the effect is not significant. The null hypothesis failed to be rejected.
There is no enough evidence to support the claim that the proportion of US teens that have some level of hearing loss differs from 20%.