As there are two senators for each state then 100 senators can be considered as 50 pairs covering 50 states. Either senator could be picked to serve on the committee. Instead of thinking in terms of senators think in terms of state representation. There are 50C5 ways of combining the representation into a committee of 5, equal to 2,118,760 (50*49*48*47*46 divided by the number of ways of arranging 5 objects, because we are only interested in combinations, not permutations). We could pick either senator for each of the five states represented, so we need to multiply this number by 2^5=32: 67,800,320.