Question

The US Senate consists of 100 members. Senate committees are to be formed so that each of the committees contains the same number of senators and each senator is a member of exactly one committee. The committees are to have more than 2 members but fewer than 50 members. There are various ways that these committees can be formed. a) What size committees are possible? b) How many committees are there for each size???

Thanks !!

Answer 1

Hi..

The US Senate consists of 100 members. Senate committees are to be formed so that each of the committees contains the same number of senators and each senator is a member of exactly one committee. The number of members of each committee is to be more than 2 but less than 50.

If each committee has N members, 100 divided by N has to be a whole number as no senator can be in more than 1 committee. The smallest number of members in a committee is 4. The number after 4 that 100 is divisible by is 5. This is followed by 10, 20 and 25.

There are 25 committees of 4 members each, 20 committees of 5 members each, 10 committees of 10 members each, 5 committees of 20 members each and 4 committees of 25 members each.

Answer 2

The US Senate consists of 100 members. Senate committees are to be formed so that each of the committees contains the same number of senators and each senator is a member of exactly one committee. The number of members of each committee is to be more than 2 but less than 50.

If each committee has N members, 100 divided by N has to be a whole number as no senator can be in more than 1 committee. The smallest number of members in a committee is 4. The number after 4 that 100 is divisible by is 5. This is followed by 10, 20 and 25.

There are 25 committees of 4 members each, 20 committees of 5 members each, 10 committees of 10 members each, 5 committees of 20 members each and 4 committees of 25 members each.