a DNA chip contain set of random hexanucleotide probes.out of 4096 probe how many will form perfect complementary duplexes with sequestionwithin the 14 nucleotide single target DNA 5'GAACTGCATTGATA3'

To determine the number of perfect complementary duplexes between the single target DNA sequence and the probes on the DNA chip, we need to consider a few factors.

First, let's calculate the number of possible hexanucleotide probes (sequences of 6 nucleotides). Since there are four possible nucleotides (A, T, C, and G), each with two possible orientations (double-stranded DNA), the total number of possible hexanucleotide probes is 4^6 = 4096.

Next, we need to figure out how many probes will form a perfect complementary duplex with the target DNA sequence. In this case, the target DNA sequence is "5'GAACTGCATTGATA3'".

To form a perfect complementary duplex, the hexanucleotide probe should have a complementary sequence to the target DNA sequence. Complementary nucleotides bind together as follows:
- A binds with T
- T binds with A
- C binds with G
- G binds with C

Therefore, for each nucleotide in the target DNA sequence, there is only one complementary nucleotide among the four possible nucleotides.

Looking at the target DNA sequence, there are 14 nucleotides in total. So, for each nucleotide position, there is only one nucleotide combination out of the four possibilities that will be complementary.

Therefore, to calculate the total number of probes that will form perfect complementary duplexes, we need to multiply the number of possible combinations of complementary nucleotides at each position.

For this particular target DNA sequence, there will be:
1 possibility for the first nucleotide position (G)
1 possibility for the second nucleotide position (A)
1 possibility for the third nucleotide position (A)
1 possibility for the fourth nucleotide position (C)
1 possibility for the fifth nucleotide position (T)
1 possibility for the sixth nucleotide position (G)
1 possibility for the seventh nucleotide position (C)
1 possibility for the eighth nucleotide position (A)
1 possibility for the ninth nucleotide position (T)
1 possibility for the tenth nucleotide position (T)
1 possibility for the eleventh nucleotide position (G)
1 possibility for the twelfth nucleotide position (A)
1 possibility for the thirteenth nucleotide position (T)
1 possibility for the fourteenth nucleotide position (A)

To find the total number of perfect complementary duplexes, we multiply all of these possibilities together:

1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1

So, out of the 4096 probes on the DNA chip, only one probe will form a perfect complementary duplex with the target DNA sequence "5'GAACTGCATTGATA3'".