You Are Attempting to Generate a Physical Map of the Bacteriophage

You are attempting to generate a physical map of the bacteriophage $\lambda$ genome using restriction enzyme digestions. You digest the phage DNA with EcoRI or NcoI or both, and observe the fragment sizes listed below. You know that bacteriophage $\lambda$ has a linear, not circular, genome. $$\begin{array} { l l l } { \text { EcoRI } } & { \text { NcoI } } & { \text { EcoRI/NcoI } } \\\hline { 21.2 \mathrm {~kb} }&{ 19.3 \mathrm {~kb} } &{ 19.3 \mathrm {~kb} } \\7.4 \mathrm {~kb} & 16.4 \mathrm {~kb} & 7.4 \mathrm {~kb} \\5.8 \mathrm {~kb} & 4.6 \mathrm {~kb} & 5.1 \mathrm {~kb} \\5.7 \mathrm {~kb} & 4.2 \mathrm {~kb} & 3.9 \mathrm {~kb} \\4.9 \mathrm {~kb} & 4.0 \mathrm {~kb} & 3.5 \mathrm {~kb} \\3.5 \mathrm {~kb} & & 2.7 \mathrm {~kb} \\& & 2.2 \mathrm {~kb} \\& & 1.9 \mathrm {~kb} \\& & 1.8 \mathrm {~kb} \\& & 0.7 \mathrm {~kb}\end{array}$$ a. How many times does the EcoRI enzyme cut the $\lambda$ DNA? How many times does the NcoI enzyme cut the $\lambda$ DNA?
b. Use the fragment size data to generate a physical map of the bacteriophage $\lambda$ genome, indicating the order and relative positions of the restriction enzyme recognition sites.