A 20 member club must have a President Vice President Secret

A 20 member club must have a President, Vice President, Secretary and Treasurer as well as a three person nominations committee. If the officers must be different people, and if no officer may be on the nominating committee, in how many ways could the officers and nominating committee be chosen? Answer the same question if officers may be on the nominating committee.

Solution

(1)

if All are different

than we suppose to choose 7 different people ( 4 officers and 3 for nominating committee)

No of ways = 20C7 = 77520

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(2)

if officers may be on the nominating committee

then

No of ways = ( no of ways to choose 4 officers)*(No of ways to choose nominating committee)

= (20C4)*(20C3)

= 4845*1140

= 5523300

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