Question #c36d4

1 Answer
Mar 31, 2017

There are 22 957 480 ways this group can be selected.


This is a situation in which we are selecting a smaller sample group from a larger group, but one where the order of selection does not matter. It makes no difference whether I am first or last on the list of group members.

So, in the choice of whether this is a permutation or a combination, the answer is - combination.

We ask for the number of combinations of 6 items taken from a group of 53:

#""_53C_6 = (53!)/ ((6!) (53-6)!# #= (53xx52xx51xx50xx49xx48)/(6xx5xx4xx3xx2xx1)#

Once done, the result is 22 957 480 ways!

(It's a lot like the question of how many poker hands of 5 cards can be dealt from a deck of 52. Again, order does not matter, so the use of combination is the correct choice. It is 2 598 960 ways.)