Question

How many ways can a teacher select a group of 4 students to sit in the front row if the class has 11 students?

Answer 1

There are 330 different ways to select a group of 4 students from a class of 11.

Step-by-step explanation:

To select a group of 4 students to sit in the front row out of 11 students, we can use the combination formula. The number of combinations of 4 students out of 11 is given by the formula C(11, 4) = 11! / (4! * (11-4)!). Evaluating this expression, we find that there are 330 different ways to select a group of 4 students from a class of 11.

Answer 2

The number of ways to select 4 students from a class of 11 is 330, calculated using the combination formula 11! / (4!7!).

Step-by-step explanation:

The given problem can be solved using the concept of combinations, which is a part of combinatorics in mathematics. Combinations are used to find out how many ways we can choose a group of items from a larger set where the order does not matter. In this case, we want to choose a group of 4 students from a class of 11 students without considering the order in which they are selected.

The number of ways to select 4 students out of 11 can be calculated using the combination formula which is nCr = n! / (r!(n-r)!), where n is the total number of items to choose from, r is the number of items to choose, n! denotes the factorial of n, and r! denotes the factorial of r.

Applying this formula to our problem:

• Total students (n) = 11
• Students to choose (r) = 4
• Combinations of selecting 4 out of 11 students (11C4) = 11! / (4!(11-4)!) = 11! / (4!7!) = (11*10*9*8) / (4*3*2*1) = 330

Therefore, there are 330 different ways the teacher can select a group of 4 students to sit in the front row from a class of 11 students.