There are 57 students in a class, how many different ways can you make a group of 5?

Question

There are 57 students in a class, how many different ways can you make a group of 5?

Answer 1

Using the function in Microsoft Excel for combinations, = COMBIN(57,5) results in 4,187,206. 

 

Manually:

_nC_r = n! / [(n-r)!r!]

_nC_{r =} 57! / [57-5)!5!] = 4,187,206

 

Answer 2

this is a combination problem

57(C)5

57!/5!(57-5)!

57!/5!52!

(57*56*55*54*53)/(5*4*3*2*1)

56/4=14, 55/5=11, 54/(3*2)=9

57*14*11*9*53=4,187,106 ways