Final answer:
There are 16653 different ways to form a subcommittee of 5 members from a congressional committee, with at least 4 of the members being representatives.
Step-by-step explanation:
The question is asking for the number of ways to form a subcommittee from a larger congressional committee composed of both senators and representatives. Since there needs to be at least four representatives on the subcommittee, we have two scenarios. The first scenario is when there are exactly four representatives and one senator, and the second scenario is when all five members are representatives.
Scenario 1: Four Representatives and One Senator
There are 15 representatives, and we want to select 4 of them: C(15, 4). There are 10 senators, and we want to select 1 of them: C(10, 1). We multiply these combinations to find the total ways for this scenario.
C(15, 4) × C(10, 1), which simplifies to 1365 × 10 = 13650.
Scenario 2: Five Representatives
There are 15 representatives, and we want to select 5 of them: C(15, 5). This simplifies to 3003.
To find the total number of ways to form the subcommittee, we add the results of the two scenarios together: 13650 + 3003 = 16653.
Therefore, there are 16653 different ways to form a subcommittee of 5 members with at least 4 representatives.