2. 15 delegates from United Nations are getting together. They will form 5 subco
ID: 2922435 • Letter: 2
Question
2. 15 delegates from United Nations are getting together. They will form 5 subcommittees of size of 4,3, 3, 3, 2 to discuss new policies. How many ways can these subcommittees be formed? French delegate and the English delegate wants to be in the same group. How many different ways can the subcommittees be formed? US delegate and the Russian delegate should not be in the same subcommittee. How many different ways can the subcommittees be formed? Amongst the countries these 15 delegates represent, there are 8 European countries, 5 Asian countries and 2 African countries. How many committees of size three are possible if the committee members must be from a different continent? a) b) c) d)Explanation / Answer
a. Number of ways to form committees
= 15C4 * 11C3 * 8C3 * 5C3
= 1365 * 165 * 56 * 10
= 126126000.
b. Since French and English delegates are in the same group let us call them together as Norman delegate.
If the Norman delegate is from the group of 4, the question would be to distribute 14 delegates among group of 3,3,3,3,2 which can be done in 14C3 * 11C3 * 8C3 * 5C3
= 364 * 165 * 56 * 10
= 33633600 ways.
If the Norman delegate is from any group of 3, the question would be to distribute 14 delegates among group of 4,3,3,2,2 which can be done in 14C4 * 10C3 * 7C3 * 4C2
= 1001 * 120 * 35 * 6
= 25225200 ways.
If the Norman delegate is from the group of 2, the question would be to distribute the remaining 13 delegates into groups of 4,3,3,3 whcih can be done in 14C4 * 10C3 * 7C3 * 4C3
= 1001 * 120 * 35 * 4
= 16816800 ways.
Total number of ways = 33633600 + 25225200 + 16816800 = 75675600.
c. If we follow the above solution and call US and Russian delegates together as Bering delegate, total number of ways to keep them together = 75675600.
=> Number of ways to put them in different groups = 126126000 - 75675600 = 50450400.
d. The European member can come in 8 ways, the Asian in 5 ways and the African in 2 ways.
=> Total committees of size 3 = 8*5*3 = 120.
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