Step-by-step explanation:
Permutations:
nP r = n!/(n + r)!
Combinations:
nCr = n!/(n - r)!r!
c - combination
p - permutations
Since in both the problems they are looking for different groups, it is a combination problem. the order in which the people were selected in each group is not important, what is required are different groups.
A.
n = 51
r = 3
51C 3 = 51! / ((51 - 3) ×3!)
51C3 = 20 825 groups
OR:
[tex]c = \frac{51}{3} \times \frac{50}{2} \times 49[/tex]
[tex]c = 20825[/tex]
B.
[tex]c = \frac{14}{4} \times \frac{13}{3} \times \frac{12}{2} \times 11[/tex]
[tex]c = 1001[/tex]
