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:
Given that the number of males in the classroom is three more than twice the number of females.
the total number of students is 57
Let x be the no of males then no of females =
Also we have 3 more than twice no of females as
This equals x
No of males = 39, no of females = 18
Answer: The correct option is triangle GDC
Step-by-step explanation: Please refer to the picture attached for further details.
The dimensions give for the cube are such that the top surface has vertices GBCF while the bottom surface has vertices HADE.
A right angle can be formed in quite a number of ways since the cube has right angles on all six surfaces. However the question states that the diagonal that forms the right angle runs "through the interior."
Therefore option 1 is not correct since the diagonal formed in triangle BDH passes through two surfaces. Triangle DCB is also formed with its diagonal passing only along one of the surfaces. Triangle GHE is also formed with its diagonal running through one of the surfaces.
However, triangle GDC is formed with its diagonal passing through the interior as shown by the "zigzag" line from point G to point D. And then you have another line running from vertex D to vertex C.
