Answer:a) 2016ways b)160ways c) 264ways
Step-by-step explanation:
a) Since selection are being made, we will use the combination rule.
If two men refuse to serve together, this means that only 1 man will be selected out of the three men that suppose to form a committee.
In order to select r objects from a pool of n objects, it is expressed as
nCr = n!/(n-r)!r!
To select 3women from 8 women, we have 8C3
To select 3men from 6men with two men refusing to serve together we have 6C(3-2) i.e 6C1
The final selection can then be made in 8C3 × 6C1 ways
= 8!/(8-3)! × 6!/(6-1)!1!
= 8!/5! × 6!/5!1!
= (8×7×6×5!/5!) × (6×5!/5!)
= 8×7×6 × 6
= 2016ways
b) Similarly if two of the women refuse to serve together, we will have;
8C1×6C3
That is only one woman is being selected out of 3.
8!/7!×6!/3!3!
= 8×6×5×4×3!/6×3!
= 8×5×4
= 160ways
c) If 1man and 1woman refuse to serve together, we will have selection of 2women and 2men from 8women and 6men to give us
8C2×6C2
= 8!/6!2!×6!/4!2!
= 8!/2!×1/4!2!
= 8×7×6×5×4!/4!×2
= 4×7×6×5
= 640ways
