Question

How many different ways can a teacher select 3 students from a class of 15 students to each perform a different classroom task?

Answer 1

Answer: 455ways

Step-by-step explanation:

This can be done according to rule of combination because it talks about selection.

In order to select r object from a pool of n objects, it is represented as nCr = n!/(n-r)!r!

Therefore to select 3 students from a class of 15students, this will give us 15C3.

15C3 = 15!/(15-3)!3!

= 15!/12!3!

= 15×14×13×12!/12!×6

= 15×14×13/6

= 455ways

This selection can be done in 455ways

Answer 2

The question is an illustration of combination

There are 455 ways of selecting the students

The number of students is 15, and the students to select are 3.

So, the number of selections is:

$*nC_r = \frac{n!}{(n -r)!r!}$

This gives

$^nC_r = \frac{15!}{(15 -3)!3!}$

Evaluate

$^nC_r = 455$

Hence, there are 455 ways of selecting the students

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