A lottery is set up in which players pick six numbers from the set 1, 2, 3, ... , 39, 40. How many different ways are there to play this lottery? (In this game the order in which the numbers are picked does NOT matter.)

Answer 1

The number of different combinations is
C(40,6) or 40!/(6!34!) = 3 838 380

Answer 2

Combination of 40 taken 6 at a time
nCr = nPr/r!
nPr = n!/(n - r)!
nCr = (n!/(n - r)!) /r!
n = 40, r = 6
40C6 = 40P6/6! = 40!/34! / 6!
= 40!/(6!*34!)
= 40*39*38*37*36*35/(6*5*4*3*2*1)
= 2,763,633,600/720
= 3,838,380

I am not a tutor but this is right IF this is a combination of 40 taken 6 at a time (I checked my math in an online calculator)

Answer 3

if,89,88,45,9,33, were selected from 1-90, what are the next five numbers to be selected.