Cards are drawn one after the other without replacement from a well shuffled pack of cards until and ace card appears. If the probability that exactly 5 cards are drawn before the first ace card appears is \(\frac{4}{49}\left(\frac{p_1 \cdot p_2 \cdot p_3}{p_4 \cdot p_5 \cdot p_6}\right),\left(p_i\right.\) is prime, \(\left.i=1,2,3,4,5,6\right)\) then \(\left(\max \left\{p_i\right\}-\min \left\{p_i\right\}\right)=\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.