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.

- Exactly two among E, J, l and C must be selected.
- If F is selected, then J cannot be selected.
- Exactly one among A and C must be selected.
- Unless A is selected, E cannot be selected,
- If and only if G is selected, D must not be selected.
- If D is not selected, then H must be selected.

The size of a team is defined as the number of members in the team.

**Q1. **Who among the following cannot be a member of a team of size 4?

- E
- H
- F
- None of THese

**Q2. **What could be the size of a team that includes both F and H?

**Q3. **In how many ways can the team of size 6 be selected, if it includes E?

**Q4. **What is the largest possible size of 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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