There are 15 students in a social studies class. Two students will be selected to present their term projects today. In how many different orders can two students be selected?

Question

valpey · Answer

15 could be picked first times the 14 who could be picked to go second.

anonymous · Answer

15c2

anonymous · Answer

take example of 3 students and 2 should be picked, combinations are (1,2),(1,3),(2,3) which is 3c2
same goes here

tester97 · Answer

im still not understanding it........

anonymous · Answer

Order seems to matter yet repetition of the same student does not so we can say it is a permutation with repetition and the formula for that is$$n^r$$ where n is the number of students and r is the number of students we choose

tester97 · Answer

so it would be? $$15^{2}$$

anonymous · Answer

Let students= 1,2,3,....15

combinations are (1,2),(1,3),(1,4)....(1,15) =========14 sets
                             (2,3),(2,4).............(2,15)==========13 sets
                              (3,4),(3,5)...........(3,15)===========12 sets

“ “ ..............................
..............................(14,15)=======================1 set

total= 14+13+12+11+10+9+8+7+6+5+4+3+2+1=105

valpey · Answer

Right. It doesn't seem to matter the order so divide my answer by two.

luigi0210 · Answer

Use the formula: $\Large C=\frac{n!}{r!(n-r)!}$

anonymous · Answer

If order does not matter then we have a combination of things where repetition and order do not matter and the formula for that is$$\frac{ (n+r-1)! }{ r!(n-1)! }$$

anonymous · Answer

N is the number of students and r is the number of students we choose

kropot72 · Answer

There are 15 choices for the first student, and each of these 15 can be combined with 14 choices for the second student. This gives 15 * 14 = 210 ways of choosing the 2 students where the order of selection matters.

tester97 · Answer

Thanks guys i think i got it now ;)

valpey · Answer

15 students can be picked to go first times 14 who could be picked to go second which is 15*14 permutations. But since order doesn't matter (we say that John goes first and Luigi goes second is the same combination as Luigi goes first and John second then we divide the permutations (15*14) by 2 to get 15*7.

valpey · Answer

But the last sentence does seem to suggest order matters

kropot72 · Answer

Yes, effectively the question says order of selection is important.

tester97 · Answer

wait now im confused :\ is it 105 different ways? or is it 210?

kropot72 · Answer

Permutations are needed, so 210 ways is correct.

tester97 · Answer

ok thanks

kropot72 · Answer

You;re welcome :)