Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?

This is a venn diagram we an directly make from the information givens -

1. three are experts in tabla but not in mridangam or ghatam,

=> only tabla = 3

2. three are experts in mridangam but not in tabla or ghatam

-> only mridangam = 3

3. one is an expert in ghatam but not in tabla or mridangam.

=> only ghatam = 1

4. two are experts in tabla and mridangam but not in ghatam,

=> only Tabla & mridangam = 2

5. one is an expert in tabla and ghatam but not in mridangam.

=> only tabla & mridangam = 1

Now, we have a total of = $3 + 3+ 1+2+1 = 10$

Therefore, we have found the distribution of all the musician

Thus, all three and only ghatam and mridangam = 0

Musicians	Instrument
A
B
C
D	T + G
E
F
G
H
I
J

Now, Clue 2 says,

D is an expert in both tabla and ghatam.

Also, from the venn , we know there is only one person expert in only tabla and ghatam

=> that person is D.

Musicians	Instrument
A
B
C
D	T + G
E
F
G
H
I	T (x)
J	T (x)

Clue 4 says,

Neither I nor J is an expert in tabla.

Musicians	Instrument
A
B
C
D	T + G
E
F
G
H	M(X)
I	G
J	T (x)

Clue 5 says,

Neither H nor I is an expert in mridangam, but only one of them is an expert in ghatam.

Now, we already know, that

I is not an expert in Tabla and this clue says, I is not expert in mridangam also

=> I will be an expert in only Ghatam

Musicians	Instrument
A
B
C
D	T + G
E
F
G
H	M(X)
I	G
J	M

From the venn , we know,

There is only one person expert in only ghatam, whom we found to be I.

Therefore, for J -

We know, J is not an expert in tabla

=> only possiblity for him = only mridangam / only ghatam or mridangam + ghatam

but, only ghatam is I

mridangam + ghatam =0

Therefore, J is an expert in only Mridangam

Musicians	Instrument
A	M
B	M
C
D	T + G
E
F
G
H	M(X)
I	G
J	M

Clue 1 says,

Both A and B are experts in mridangam, but only one of them is also an expert in tabla.

=> one of A and B = only mridangam and other is Mridangam + tabla

Musicians	Instrument
A	M
B	M
C
D	T + G
E
F	T
G	T
H	M(X)
I	G
J	M

Clue 3 says,

Both F and G are experts in tabla, but only one of them is also an expert in mridangam.

=> One of F and G is an expert in only tabla and other in Tabla and mridangam.

=> one of A and B = only mridangam and other is Mridangam + tabla

Musicians	Instrument
A	M
B	M
C
D	T + G
E
F	T
G	T
H	T
I	G
J	M

Now, we know there are 2 musicians expert in Tabla and mridangam

which , we have found to be:

1. one of A or B.

2. One of F or G.

Also, Tabla + ghatam = 1 , which is D.

Therefore, For H :

We know, H can't be an expert in mridangam

Therefore, he will be an ecpert in only tabla or only ghatam

But only ghatam is I

therefore, H is an expert in only Tabla.

Musicians	Instrument
A	M
B	M
C
D	T + G
E
F	T
G	T
H	T
I	G
J	M

Now, we know, there are 3 people experts in only tabla

One we have found to be H

other will be one among G or H

Therefore, only possibility for third person is one among C or E.

And, other of C and E will be an expert in both Tabla and mridangam.

Musicians	Instrument
A	M
B	M
C
D	T + G
E
F	T
G	T
H	T
I	G
J	M

It can only be from A/B, F/G

∴ C and E is the correct options