Answer:
Step-by-step explanation:
When choosing 5 objects without replacement from 15 distinct objects, and the order of the choices is not relevant, this is a combination problem.
The formula for combinations is:
�
(
�
,
�
)
=
�
!
�
!
(
�
−
�
)
!
C(n,k)=
k!(n−k)!
n!
Where:
�
n is the total number of distinct objects (in this case, 15)
�
k is the number of objects to be chosen (in this case, 5)
�
!
n! denotes the factorial of
�
n, which is the product of all positive integers up to
�
n
Using this formula, we can calculate the number of ways to choose 5 objects from 15:
�
(
15
,
5
)
=
15
!
5
!
(
15
−
5
)
!
C(15,5)=
5!(15−5)!
15!
�
(
15
,
5
)
=
15
!
5
!
10
!
C(15,5)=
5!10!
15!
�
(
15
,
5
)
=
15
×
14
×
13
×
12
×
11
5
×
4
×
3
×
2
×
1
C(15,5)=
5×4×3×2×1
15×14×13×12×11
�
(
15
,
5
)
=
360360
120
C(15,5)=
120
360360
�
(
15
,
5
)
=
3003
C(15,5)=3003
So, there are 3003 ways to choose 5 objects from 15 distinct objects without replacement when the order of the choices is not relevant.
