The total number of progeny obtained through dihybrid cross of Mendel is 1280 in \( F_2 \) generation. How many are recombinants in this?
Show Hint
For dihybrid crosses, remember the classic Mendelian \( 9:3:3:1 \) phenotypic ratio. Recombinants are those that differ from both parental combinations — typically 6 out of 16 parts or \( \frac{3}{8} \) of the total in \( F_2 \).
Step 1: Understand the Dihybrid Cross
In a typical Mendelian dihybrid cross (e.g., \( AaBb \times AaBb \)), the phenotypic ratio in the \( F_2 \) generation is:
\[
9 : 3 : 3 : 1
\]
This corresponds to:
\begin{itemize}
\item 9 parts: both dominant traits (A-B-) — Parental type
\item 3 parts: dominant A, recessive b (A-bb) — Recombinant
\item 3 parts: recessive a, dominant B (aaB-) — Recombinant
\item 1 part: both recessive traits (aabb) — Parental type
\end{itemize}
Step 2: Determine Total Recombinant Ratio
Out of total 16 parts:
\[
\text{Recombinant types} = 3 + 3 = 6
\quad \text{So, recombinant ratio} = \frac{6}{16} = \frac{3}{8}
\]
Step 3: Calculate Number of Recombinants
Total number of progeny = 1280
\[
\text{Number of recombinants} = \frac{3}{8} \times 1280 = 480
\]
\[
\boxed{480}
\]
