The number of different groups of students that can be formed from 16 students depends on the size of the groups being formed. If you are looking for all possible combinations of groups of any size (from 1 to 16), you can use the formula for combinations. The total number of combinations would be (2^{16} - 1) (subtracting 1 to exclude the empty group), which equals 65,535 different groups. If you specify a particular group size, the calculation would be different.
20 x 19 x 18/3 x 2 = 1,140 groups
if order does not matter then, (23x22x21x20x19)/(5x4x3x2x1) = 33,649
18
only one with two cars left
To find the number of different groups of 4 that can be made from 17 students, you can use the combination formula, which is given by ( C(n, r) = \frac{n!}{r!(n-r)!} ). In this case, ( n = 17 ) and ( r = 4 ). Therefore, the calculation is ( C(17, 4) = \frac{17!}{4!(17-4)!} = \frac{17!}{4! \times 13!} = \frac{17 \times 16 \times 15 \times 14}{4 \times 3 \times 2 \times 1} = 2380 ). Thus, there are 2,380 different groups of 4 that can be formed from 17 students.
20 x 19 x 18/3 x 2 = 1,140 groups
There are 247 groups comprising 2 or more students.
23 x 22 x 21 x 20/4 x 3 x 2 = 8,855 groups
30C8 = 5,852,925
if order does not matter then, (23x22x21x20x19)/(5x4x3x2x1) = 33,649
75
2 groups. 2 x 3= 6
18
To find the number of different groups (a) within a larger group (b), use the formula b!/a!.(b-a)! where the ! sign indicates "factorial". In your problem b = 21 and a = 5 so we have 21!/(5!.16!) this simplifies to 21.20.19.18.17/5.4.3.2 cancelling leaves 21.19.3.17 ie 20349
There are 10560 possible committees.
There are 27 choose 25 ways, which is equivalent to 27! / (25!(27-25)!) = 351 possible different groups of 25 people that can be formed from a total of 27 people.
only one with two cars left