Suppose a committee of the UN contains 193 diplomats, exactly one representing each of the 193 nation states. In how many ways can a subcommittee of 20 be selected a. If the representative from Switzerland must be on the committee? b. If exactly 5 members must be from the 54 African states? c. If a head of state wants to receive all 193 diplomats and greet them in person, in how many different ways can they be lined up to be received by her? Give all answers in terms of combinations, permutations or factorials. Solution There are 193 nation states. A subcommitte of 20 to be selected from 193 one from each state. a) 1 choice is restricted to be from Switzerland. Hence other choices are 19 out of 192 remaining. No of ways = 193C19 = 87656719647088979023375200 = 8.77x1025 ---------------------------------------------------------------------------------------------------------------- b) 5 from 54 african states and other 15 from 139 states. no of ways = 54C5(139C15) c) no of ways 193 can be arranged = 193! ways.

1. Suppose a committee of the UN contains 193 diplomats, exactly one representing each of the 193
nation states. In how many ways can a subcommittee of 20 be selected
a. If the representative from Switzerland must be on the committee?
b. If exactly 5 members must be from the 54 African states?
c. If a head of state wants to receive all 193 diplomats and greet them in person, in how many
different ways can they be lined up to be received by her?
Give all answers in terms of combinations, permutations or factorials.
Solution
There are 193 nation states.
A subcommitte of 20 to be selected from 193 one from each state.
a) 1 choice is restricted to be from Switzerland. Hence other choices are 19 out of 192 remaining.
No of ways = 193C19 = 87656719647088979023375200 = 8.77x1025
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b) 5 from 54 african states and other 15 from 139 states.
no of ways = 54C5(139C15)
c) no of ways 193 can be arranged = 193! ways