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
The expression representing N students divided into groups of six can be written as ( \frac{N}{6} ). This expression indicates how many complete groups of six can be formed from N students. If there are any remaining students after forming the groups, they would not be counted in this expression as it only considers complete groups.
18
To find the number of different groups of 3 students that can be selected from 10 students, we use the combination formula: ( C(n, r) = \frac{n!}{r!(n-r)!} ). Here, ( n = 10 ) and ( r = 3 ), so the calculation is ( C(10, 3) = \frac{10!}{3!(10-3)!} = \frac{10 \times 9 \times 8}{3 \times 2 \times 1} = 120 ). Therefore, there are 120 different groups of 3 students that can be formed.
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