A team is to be selected from among ten persons — A, B, C, D, E, F, G, H, I and J — subject to the following conditions.
The size of a team is defined as the number of members in the team.
Given,
- E,J, l,C—>EJ/El/EC/Jl/JC/IC
- F,J—>F/J/0
- A, C—>A/C
- E —> A
- (V) G, D —> G / D
- D,H—>H/D/HD
From (ii), among F and J, only J can be selected or only F can be selected or none of them can be selected.
From (iv), among A and E, either both can be selected or none of them can be selected.
Q1. The following teams includes E or H or F but violate none of the given conditions.
(1) E, A, I, G
(2) J, H, C, D
(3) F, l, C, D
Therefore, right answer is option (4)
Q2. As both F and H are selected.
Exactly two among E, l and C must be selected and exactly one among G and D must be selected.
Therefore, the team which includes both F and H, cannot be of the size 3 or 4.
The maximum possible size of the team is 7.
It cannot be 8.
But, the size of the team could be 5, as follows: F, H, I, C, G
Q3. If E is selected, then A must also be selected.
Therefore, C cannot be selected.
In the following ways, the team of 6 can be selected.
(1) A, E, J, G/D, H, B 2 ways
(2) A, E, I, F, G/D, H ----- 2ways
(3) A, E, I, G/D, H, B 2 ways
(4) A, E, I, F, D, B
Therefore, there are a total of 7 ways.
Q4. To maximize the size of the team, we should follow the steps given below.
(i) Among F and J, let us select F.
(ii) Among A and C, let us select A.
(iii) As A is selected let us select E also.
(iv) Among G, D and H, let us select D and H or G and H.
(v) Among E, J, l and C, as E is already selected, and J and C cannot be selected. I should be selected.
(vi) Let us include B also in the team.
Therefore, the possible team is F, A, E, D. H, l, B.
Hence, the maximum possible size of the team is 7.
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