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.
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Answer:
Step-by-step explanation:
The standard form for this function is
y = Asin(Bx - C) + D where
A is the amplitude,
B is used to find the period in the formula ,
C is used to find the phase shift in the formula ,
and D is the midline which either moves the function up or down from its natural midline of 0.
We have no given phase shift, so there is no C value. The amplitude is easy; we just fill in A as 4. The period is another story:
and we solve for B by cross multiplying:
3πB = 4π and
so
so the function is