How many different committees of 40 senators can be formed i

How many different committees of 40 senators can be formed if the two senators from the same state (50 states in all) are considered identical? Use generating functions.

Solution

There is no possibility, under any circumstances, of two senators from the same state being regarded as identical.

I am assuming the twit who wrote this meant that
(1) no more than one senator from any state would be on the committee; and
(2) they\'re interested in the number of possible sets of represented states, without regard to which senator represents each state.
Whether that assumption is correct or not, the statement made is utter nonsense.

With the stated assumption (and also the assumption that this refers to the Senate of the U.S.A., which has 50 states), the number of possible combinations of states is
C(50,40) = 50! / (40! 10!)
= 50*49*48*47 * 46*45*44 * 43*42*41 / (10*9*8*7*6 * 5*4*3*2*1)
= 49 * 47 * 46 *5 * 11 * 43 * 41
= 10,272,278,170