six students of different heights are going to march in a single file in a parade carrying flags. the order in which they march is to be randomly selected. what is the probability that they will march in order of height from shortest to tallest.
can you please describe the steps taken to reach your answer.
There are six ways of choosing who goes first, then five for who goes next, etc.
The number of possible arrangements is 6*5*4*3*2*1 = 6! = 720
Only one of those arrangements is the one you want.
The probability is therefore 1/720
Sure, I'd be happy to help! The probability of the six students marching in order of height from shortest to tallest can be calculated by considering the number of favorable outcomes divided by the total possible outcomes.
Let's break down the steps:
Step 1: Determine the number of favorable outcomes.
In this case, the favorable outcome is the specific order of the students from shortest to tallest. Since there are six students, there is only one favorable outcome.
Step 2: Determine the total possible outcomes.
The total possible outcomes can be calculated by finding the number of ways the six students can be arranged in a random order. This can be done using the concept of permutations, which is denoted as nPr.
In this case, we have six students, so the total possible outcomes can be calculated as 6P6, which equals 6!.
Step 3: Calculate the probability.
Now that we have the number of favorable outcomes and the total possible outcomes, we can calculate the probability using the formula:
Probability = favorable outcomes / total possible outcomes
In this case, the probability is 1 (the number of favorable outcomes) divided by 6! (the total possible outcomes).
Therefore, the probability that the six students will march in order of height from shortest to tallest is 1/(6!) or 1/720.
Of course, keep in mind that this assumes the students' heights are unique and that all orders of the students are equally likely.
To calculate the probability that six students will march in order of height from shortest to tallest, we need to determine two things: the total number of possible ways the students can be arranged, and the number of ways they can be arranged in the desired order.
Step 1: Determine the total number of possible arrangements.
There are six students, so there are six possible choices for the first person in line, five choices for the second person, four choices for the third person, and so on. Therefore, the total number of possible arrangements is 6 x 5 x 4 x 3 x 2 x 1 = 720.
Step 2: Determine the number of arrangements in the desired order.
Since we want the students to march from shortest to tallest, there is only one specific order that satisfies the condition. Therefore, the number of arrangements in the desired order is 1.
Step 3: Calculate the probability.
To calculate the probability, we divide the number of arrangements in the desired order by the total number of possible arrangements:
Probability = number of arrangements in the desired order / total number of possible arrangements
Probability = 1 / 720
Therefore, the probability that the six students will march in order of height from shortest to tallest is 1/720.
Sure! To find the probability that the six students will march in order of height from shortest to tallest, we need to determine the total number of possible orders in which they can march, as well as the number of orders that satisfy the given condition.
Step 1: Find the total number of possible orders
Since there are six students, there are 6! (6 factorial) possible orders in which they can march. This is because for the first position in the parade, there are six choices, for the second position there are five remaining choices, for the third position there are four remaining choices, and so on, until there is only one choice left for the last position. Therefore, 6! = 6 x 5 x 4 x 3 x 2 x 1 = 720 possible orders.
Step 2: Find the number of orders that satisfy the condition
For the students to march in order of height from shortest to tallest, there is only one specific order that meets this condition. Since the students have different heights, there is no other possible variation of this order. Therefore, there is only 1 order that satisfies the given condition.
Step 3: Calculate the probability
Finally, we divide the number of orders that satisfy the condition by the total number of possible orders to find the probability.
Probability = (Number of orders that satisfy the condition) / (Total number of possible orders)
= 1 / 720
= 0.00139 (rounded to five decimal places)
Therefore, the probability that the six students will march in order of height from shortest to tallest is approximately 0.00139.