Answer:
364 ways
Step-by-step explanation:
To calculate the number of ways 5 students can be chosen from a group of 16, you can use the combination formula, which is denoted as "n choose k" and calculated as:
Number of combinations
=
(
�
�
)
=
�
!
�
!
⋅
(
�
−
�
)
!
Number of combinations=(
k
n
)=
k!⋅(n−k)!
n!
Where:
�
n is the total number of students (16 in this case).
�
k is the number of students to be chosen (5 in this case).
!
! denotes factorial, which means the product of all positive integers less than or equal to that number.
So, plugging in the values:
(
16
5
)
=
16
!
5
!
⋅
(
16
−
5
)
!
(
5
16
)=
5!⋅(16−5)!
16!
(
16
5
)
=
16
!
5
!
⋅
11
!
(
5
16
)=
5!⋅11!
16!
Now, let's calculate:
(
16
5
)
=
16
×
15
×
14
×
13
×
12
5
×
4
×
3
×
2
×
1
(
5
16
)=
5×4×3×2×1
16×15×14×13×12
(
16
5
)
=
43680
120
(
5
16
)=
120
43680
(
16
5
)
=
364
(
5
16
)=364
So, there are 364 ways to choose 5 students from a group of 16 to go on the field trip.
