In how many ways can 4 students be selected from a group of 10?
Practice Questions
1 question
Q1
In how many ways can 4 students be selected from a group of 10?
210
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The number of ways to select 4 students from 10 is C(10,4) = 210.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 4 students be selected from a group of 10?
Solution: The number of ways to select 4 students from 10 is C(10,4) = 210.
Steps: 11
Step 1: Understand that we want to choose 4 students from a total of 10 students.
Step 2: Recognize that the order in which we select the students does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is C(n, r) = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In our case, n = 10 (total students) and r = 4 (students to select).
Step 5: Plug the values into the formula: C(10, 4) = 10! / (4! * (10 - 4)!) = 10! / (4! * 6!).
Step 6: Calculate 10! = 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1, but we can simplify it by canceling out 6! in the denominator.
