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