In how many ways can a committee of 5 members be formed from 10 candidates so as to exclude the youngest of it includes the oldest. PS- the answer is 196 but idk how
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Answer:
There are two different ways of forming the committee
(i) oldest may be included
(ii) oldest may be excluded
(i) If oldest is included, then youngest has to be excluded and we are to select 4 candidates out of 8. This can be done in
8
C
4
=
4!4!
8!
=
4×3×2
8×7×6×5
=70 ways
(ii) If oldest is excluded, then we are to select 5 candidates from 9 which can be done in
9
C
5
=
5!4!
9!
=
4×3×2×1
9×8×7×6
=126
Hence, the total number of ways in which committee can be formed =126+70=196.
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