An experiment involves 30 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants are possible?
Question
An experiment involves 30 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants are possible?
Solution
To solve this problem, we need to use the concept of combinations in mathematics. A combination is a selection of items where order does not matter.
The formula for combinations is:
C(n, k) = n! / [k!(n-k)!]
where:
- n is the total number of items,
- k is the number of items to choose,
- "!" denotes factorial, which means multiplying all positive integers up to that number.
In this case, n = 30 (the total number of participants) and k = 4 (the number of participants in each group).
So, the number of possible groups is:
C(30, 4) = 30! / [4!(30-4)!]
Calculating the factorials:
30! = 30 × 29 × 28 × ... × 3 × 2 × 1 4! = 4 × 3 × 2 × 1 (30-4)! = 26! = 26 × 25 × ... × 3 × 2 × 1
Substituting these into the formula gives:
C(30, 4) = 30! / [4! × 26!]
This simplifies to:
C(30, 4) = (30 × 29 × 28 × 27) / (4 × 3 × 2 × 1)
Calculating this gives:
C(30, 4) = 27,405
So, there are 27,405 possible groups of 4 participants that can be formed from 30 participants.
Similar Questions
(a) 56 athletes are running a race. A gold medal is to be given to the winner, a silver medal is to be given to the second-place finisher, and a bronze medal is to be given to the third-place finisher. Assume that there are no ties. In how many possible ways can the 3 medals be distributed?(b) An experiment involves 31 participants. From these, a group of 4 participants is to be tested under a special condition. How many groups of 4 participants are possible?
This year, 96 students signed up for the group talent contest. If all the groups had the same number of students, how many groups could be formed? A. 3 groups B. 4 groups C. 5 groups D. Either 3 groups or 4 groups
In designing an experiment involving a treatment applied to 4 test subjects, researchers plan to use a simple random sample of 4 subjects selected from a pool of 31 available subjects. (Recall that with a simple random sample, all samples of the same size have the same chance of being selected.) Answer the questions below.a.) How many different simple random samples are possible? b.) What is the probability of each simple random sample in this case? (Type an integer or a simplified fraction.)
A teacher has to choose the maximum number of different groups comprising of four students from a total of six students. Of these groups, in how many groups will one particular student be a part of?Choices:- 10 20 15 17
Find the probability that fewer than four of them fail the test.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.