1,820 different 4-person groups can be made. We can make 455 different groups of 3 students and 3,003 different groups of 5 students.
How many different combinations are there?
The total number of different groups of 4 elements that we can make out of a total of 16 is given by:
[tex]C(16, 4) = \frac{16!}{(16 - 4)!*4!} = \frac{16*15*14*13}{4*3*2*1} = 1,820[/tex]
1,820 different 4-person groups can be made.
Now, if a person leaves the group, now we have 15 students, and we can make:
[tex]C(15, 3) = \frac{15!}{(15 - 3)!*3!} = 455[/tex]
So we can make 455 different groups of 3 students.
[tex]C(15, 5) = \frac{15!}{(15 - 5)!*5!} = 3,003[/tex]
We can make 3,003 different groups of 5 students.
If you want to learn more about combinations:
https://brainly.com/question/11732255
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