Question

You just got a free ticket for a boat ride, and you can bring along 222 friends! unfortunately, you have 555 friends who want to come along. how many different groups of friends could you take with you?

Answer 1

The solution would be like this for this specific problem:

Given: n (objects) = 555

r (sample) = 222

C (n, r) = C (555, 222)

`(555!)/((222!(555−222)!)`

= 5.711721253E+160

555 nCr 222 = 57117212533893475550611833988747426677146826761372763318735580307112179904951840423061305996599436547564283744124639707802221628272320974048311192258663900904000

So there are 57117212533893475550611833988747426677146826761372763318735580307112179904951840423061305996599436547564283744124639707802221628272320974048311192258663900904000 different groups of friends that you could take with you.

Answer 2

We need to find out how many different combinations of 222 object (friends) from a set of 555 object (friends).
r=222
n=555
The formula for calculating the number of combinations is:
C=n!/r!*(n-r)!
C=555!/222!*333!=555*554*553*......333!/222!*333!=555*554*553*..334/222*221*220*...