1. **State the problem:** We need to find the number of permutations of selecting four leadership positions: Majority Leader and Assistant Majority Leader from 90 Democrats, and Minority Leader and Assistant Minority Leader from 70 Republicans. 2. **Formula used:** The number of permutations of selecting $k$ positions from $n$ people is given by the permutation formula: $$P(n,k) = \frac{n!}{(n-k)!}$$ 3. **Apply the formula for Democrats:** We select 2 positions (Majority Leader and Assistant Majority Leader) from 90 Democrats: $$P(90,2) = \frac{90!}{(90-2)!} = 90 \times 89 = 8010$$ 4. **Apply the formula for Republicans:** We select 2 positions (Minority Leader and Assistant Minority Leader) from 70 Republicans: $$P(70,2) = \frac{70!}{(70-2)!} = 70 \times 69 = 4830$$ 5. **Calculate total permutations:** Since these selections are independent, multiply the two results: $$8010 \times 4830 = 38,688,300$$ 6. **Final answer:** There are **38,688,300** permutations of these four leadership positions. This means there are over 38 million ways to assign these leadership roles given the group sizes.