(ii) In how many ways can a President, Vice President and a Secretary be selected?
(i) Out of 25 members only 3 officers can be selected.
number of ways of selecting 3 officers = 25 C3
(ii) To select a president, we have 9 options
to select vice president, we have 8 options
to select s ecretary, we have 7 options
total number of ways = 9 ⋅ 8 ⋅ 7 = 504
Hence the answer is 504.
Problem 3 :
How many ways a committee of six persons from 10 persons can be chosen along with a chair person and a secretary?
Out of 10 members, we have to select a chair person. So we have 10 options to select a chair person. 9 options to select a secretary.
After selecting a chair person and secretary, we have 8 member. Out of 8, we have to select 4 persons.
Hence the answer is (10 ⋅ 9) 8 C4
How many different selections of 5 books can be made from 12 different books if,
(i) Two particular books are always selected?
(ii) Two particular books are never selected?
(i) Since two particular books are always selected, we may select remaining 3 books out of 10 books.
10 C3 = 10!/(7! 3!) = (10 ⋅ 9 ⋅ 8)/( 3 ⋅ 2 )
Hence the answer is 120.
(ii) Since two particular books are never selected, we may select 5 books out of 10 books.
10 C5 = 10!/(5! 5!) = (10 ⋅ 9 ⋅ 8 ⋅ 7 ⋅ 6 )/(5 ⋅ 4 ⋅ 3 ⋅ 2 )
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