If a committee of 4 students is selected from a class of 16 students, how many ways can this be done?
This is a case of choosing without replacement, and order does not count.
Number of ways
= nCr
= n!/(r!(n-r)!)
=16!/(4!12!)
To find the number of ways a committee of 4 students can be selected from a class of 16 students, we can use the concept of combinations.
The formula for combinations is given by:
nCr = n! / (r!(n-r)!), where n is the total number of options and r is the number of options to be selected.
In this case, we want to select 4 students from a class of 16 students. So, we'll use the formula:
16C4 = 16! / (4!(16-4)!)
= 16! / (4!12!)
The exclamation mark denotes factorial. It means the product of all positive integers up to the given number.
Now, we can compute the value of this expression to find the number of ways:
16! = 16 x 15 x 14 x 13 x 12!
so, 16! / 4! = 16 x 15 x 14 x 13
Simplifying further:
16C4 = (16 x 15 x 14 x 13) / (4 x 3 x 2 x 1)
= 14,560
Therefore, there are 14,560 different ways to select a committee of 4 students from a class of 16 students.